1

Alberto TALIERCIO DIPARTIMENTO DI

INGEGNERIA CIVILE E AMBIENTALE

POLITECNICO DI MILANO

SUMMARIES OF PUBLICATIONS Papers and books are classified according to the following codes: LA1: Books. LA2: Books with international diffusion. LE1: Editing of books. LE2: Editing of books with international diffusion. RV1: Notes and papers published in ISI-classified or equivalent journals. RV2: Notes and papers published in other journals. CL1: Notes and papers published in books with international diffusion. CL2: Notes and papers published in books. CV1: Notes and papers published in proceedings of international conferences. CV2: Notes and papers published in proceedings of national conferences.

2

Paper No. 1 RV2

Pandolfi A., Taliercio A.

NUMERICAL ANALYSIS OF NO-TENSION MATERIAL ARCHES UP TO COLLAPSE AND COMPARISON WITH EXPERIMENTAL RESULTS (in Italian) Studi e Ricerche, Corso di Perfezionamento per le Costruzioni in Cemento Armato, Politecnico di Milano, Ed. Italcementi (Bergamo), Vol. 6, 1984, pp. 85-118.

The aim of this paper is to study the behaviour of no-tensile material arches and vaults (plane concrete, masonry) in the elastic-plastic domain and up to failure. The basic assumptions of the classic limit analysis are briefly reviewed. As it is well known, limit analysis gives only information concerning the ultimate load bearing capacity of the structure, but cannot describe the stress evolution. Two finite element models have been developed, suitable to the description of the behaviour of continuous or voussoir beams and arches: the former is a two noded “contact” element; the latter is a plane, isoparametric, six-noded “beam” element. The “contact” element, modeling joint sections, is advantageous in block structures, in which the joints are preferential failure sections; the model allows to concentrate the plastic deformations in the joints and to consider blocks as indefinitely elastic. The six-noded element is particularly fit to the study of continuous beams and arches. The elastic matrix is formulated so as to take into account the basic assumptions of De Saint Venant theory. For structures having preferential failure sections, the first model is particularly appropriate. but. the second model becomes advantageous when it is necessary to verify the yield condition in terms of local "stress" variables. The results obtained by means of the numerical analysis up to failure of two structures are shown. The former is a voussoir arch, whose joints are modeled by means of “contact" elements; the latter is a masonry vault, reinforced with a plane concrete shell, discretized with six-noded elements. The experimental results for both structures are compared with the numerical results obtained by the authors. The voussoir arch exhibits discrepancies between numerical and experimental results: this fact is critically discussed and partially justified. The authors stress that the joint compressive strength should not be taken as unlimited (as commonly assumed in limit analysis of block structures), because this assumption often leads to unsafe results. The agreement between the numerical and the experimental results for the reinforced vault is very satisfactory. The use of isoparametric, six-noded elements, and of a nonlinear computer program, solving the elastic-plastic incremental problem by means of an algorithm of Mathematical Programming, enables the authors to obtain (at a lower computational cost) more accurate results than those of the original research program.

KEY WORDS: arches, masonry, concrete, finite elements, plasticity, limit analysis, mathematical programming.

Paper No. 2 RV1

Sacchi Landriani G., Taliercio A.

3

NUMERICAL ANALYSIS OF THE FLAT-JACK TEST ON MASONRY WALLS Journal de Mécanique Théorique et Appliquée, Vol. 5, No. 3, pp. 313-339, 1986.

The flat jack test on masonry walls (previously subjected to experimental trials) has been numerically simulated using a finite element non-linear computer program. A failure criterion was adopted such as to closely resemble the envelope of experimental resistance domains (obtained by other Authors), that vary depending on the inclination of the principal stresses to the bed jointing plane. Results obtained are generally in agreement with experimental findings, which proves the numerical model used to be reliable. Consequently, numerical analyses highlighted some aspects of the test, which had gone unnoticed in the laboratory and which contribute to a more accurate interpretation of the test itself.

KEY WORDS: flat jack, masonry, finite elements, plasticity.

Paper No. 3 RV1

Sacchi Landriani G., Taliercio A.

A NOTE ON FAILURE CONDITIONS FOR LAYERED MATERIALS Meccanica, Vol. 22, No. 2, pp. 97-102, 1987.

Some failure conditions for heterogeneous layered media, formed by two alternating homogeneous materials, are presented. The failure criteria have been obtained by a homogenization procedure, on the basis of the criteria of the materials forming the layered medium. The paper deals with layers formed by Mohr-Coulomb’s type materials (the cases of cohesionless materials or materials provided by the same friction angle are discussed), as well as with layers undergoing the maximum tensile stress criterion. Theoretical predictions are in good agreement with the experimental results obtained by other authors on layered sands and laminated rocks.

KEY WORDS: homogenization, limit analysis, layered rock, layered sand.

Paper No. 4 RV1

Rovati M., Taliercio A.

ON THE ADJOINT CONSTITUTIVE LAW IN NONLINEAR ELASTIC OPTIMAL DESIGN Meccanica, Vol. 22, No. 3, pp. 150-156, 1987.

This work is concerned with a structural optimization problem, formulated in quite general terms, involving an elastic nonlinear isotropic three-dimensional continuum. The resolution is approached through a variational technique (Lagrange multiplier method); this technique yields, in addition to the optimality condition, a set of equations which can be interpreted as governing equations of

4

another structural problem, “adjoint” to the given one. The constitutive law of the adjoint problem is studied in detail and the differences between the real and the adjoint constitutive laws are pointed out. In particular, it is shown that the material of the adjoint problem is orthotropic and its principal directions of orthotropy are determined. Finally. the results obtained are specialized to a «compliance» optimization problem for elastic nonlinear plates in bending; the difference between the present case and the already known case where the plate is linearly elastic is discussed.

KEY WORDS: optimization, nonlinear elasticity, Lagrange multipliers, anisotropy.

Paper No. 5 RV1

Taliercio A., Sacchi Landriani G.

A FAILURE CONDITION FOR LAYERED ROCK Int. J. Rock Mech. Min. Sci., Vol. 25, No. 5, pp. 299-305, 1988.

The present paper covers a failure criterion for heterogeneous layered media, based on the assumption that each of their components follows a Mohr-Coulomb type strength condition. The “homogenization technique” employed enables the formulation of a failure condition defined by four strength parameters; the procedure for the identifìcation of the parameters, starting from experimental data, is outlined. The model enables the description with fair accuracy of the ultimate behaviour of layered rocks submitted to triaxial tests, varying both the orientation of the principal stresses to the layers and the confining pressure.

KEY WORDS: homogenization, limit analysis, layered rock, macroscopic strength, anisotropy.

Paper No. 6 CL2

Salençon J., Sacchi Landriani G., de Buhan P., Taliercio A.

MACROSCOPIC FAILURE CRITERIA FOR LAYERED MATERIALS (in Italian) Commemorative volume in honour of Prof. Giulio Ceradini, Dept. of Structural and Geotechnical Engineering, University of Rome ‘La Sapienza’, pp. 629-640, 1988.

The aim of the work is to define a strength criterion for layered materials, constituted by the regular superposition of layers which can be individually assumed to be homogeneous and isotropic. To this end, the homogenization theory for heterogeneous periodic media is applied to limit analysis. Dealt with are the cases of purely cohesive components, components endowed with cohesion and friction, as well as layers with friction alternated with reinforcing metallic strips (reinforced soils). The validity of the theoretical results obtained is checked through comparisons with experimental results of other researchers.

KEY WORDS: homogenization, limit analysis, layered media, reinforced soils,

5

macroscopic strength, anisotropy.

Paper No. 7 RV2

de Buhan P., Taliercio A.

MACROSCOPIC STRENGTH CRITÈRION FOR FIBER COMPOSITE MATERIALS (in French) C.R. Acad. Sci., t. 307, Série II, pp. 227-232, Paris, 1988.

An explicit formulation of the macroscopic strength criterion for a fiber reinforced composite material is derived from the yield design homogenization theory. It is shown in particular that, when taking into account a failure condition at the fìber-matrix interfaces, the experimental identification of which is very simple, a very good agreement is obtained between the theoretical predictions and the available experimental data.

KEY WORDS: homogenization, yield design, fiber reinforced composites, macroscopic strength.

Paper No. 8 CV1

Sacchi Landriani G., Taliercio A.

STRENGTH CRITERIA FOR FIBER REINFORCED COMPOSITE MATERIALS in ‘Composite Material Technology’, D. Hui & T.J. Kozik (Eds.), pp. 49-55, ASME, New York, 1989.

The ultimate behaviour of fiber reinforced composites is frequently described by phenomenological failure criteria, whose origin is fundamentally empirical. A theoretical tool for defining in a rigourous way a strength criterion for this class of materials ìs provided by the homogenization theory, applied to the limit analysis. Such a criterion is called 'macroscopic', since it describes the overall strength of the composite material, starting from the knowledge of the strength properties of its constituents (matrix and fibers) and of their geo- metrical arrangement. Furthermore, the possibility of failure at the fiber-matrix interface can easily be taken into account. By means of this model, the ultimate behaviour of several composites subjected to uniaxial and biaxial stress was described; the theoretical results obtained are in good agreement with available experimental data. This approach provides a particularly suitable method for designing new composite materials according to strength requirements.

KEY WORDS: homogenization, limit analysis, fiber reinforced composite materials, macroscopic strength.

Paper No. 9 LA1

Taliercio A.

6

STUDY OF THE ELASTIC AND FAILURE BEHAVIOUR OF FIBER REINFORCED COMPOSITES AND COMPOSITE STRUCTURAL ELEMENTS (in Italian) PhD Thesis in Structural Engineering, Politecnico di Milano, February 1989.

Paper No. 10 CV2

Taliercio A.

BILATERAL BOUNDING OF THE MACROSCOPIC STRENGTH DOMAIN OF A FIBER-REINFORCED MATERIAL (in Italian) Proc. X Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Pisa (I), October 2-5, 1990, pp. 141-146.

The macroscopic strength domain or a composite material reinforced by long, parallel fibers is, in general, unknown but for its theoretical definition. In this note it is shown how a homogenization technique applied to yield design theory a1lowed to derive (in the space or macroscopic stresses) two domains, which are a lower and an upper bound to the real strength domain. The dependence or these domains on the fiber content and on the shape or the fiber array is discussed.

KEY WORDS: homogenization, limit analysis, fiber reinforced composite materials, macroscopic strength.

Paper No. 11 CV1

de Buhan P., Salençon J., Taliercio A.

LOWER AND UPPER BOUND ESTIMATES FOR THE MACROSCOPIC STRENGTH CRITERION OF FIBER COMPOSITE MATERIALS in ‘Inelastic deformation of composite materials’, G.J. Dvorak (Ed.), Springer-Verlag, New York, pp. 563-580, 1991.

The formulation of a homogenization procedure within the framework of the yield design theory makes it possible to derive a strength criterion for a fiber composite material in a rigorous way, from the only definitions of the strength properties of the constituents (matrix and fibers) and of their geometrical, structural and voluminal arrangement. Making use of both yield design static and kinematic approaches, quite simple analytical lower and upper bounds estimates are obtained for a unidirectional fiber composite. A detailed analysis of those estimates is carried through in the specific case when the composite is subjected to a uniaxial solicitation or to plane strain conditions parallel to the fibers direction.

KEY WORDS: homogenization, limit analysis, fiber reinforced composite materials, macroscopic strength.

7

Paper No. 12 CV1

Rovati M., Taliercio A.

OPTIMAL ORIENTATION OF THE SYMMETRY AXES OF ORTHOTROPIC 3-D MATERIALS in ‘Engineering optimization in design processes’, H.A. Eschenauer, C. Mattheck & N. Olhoff (Eds.), Lecture Notes in Engineering, Springer-Verlag, Heidelberg (D), pp. 127-154, 1991.

Assuming the elastic energy as a meaningful measure of the global stiffness (or flexibility) of an elastic body, in this paper the interest is paid to the determination of those local orientations of the material symmetry axes in an orthotropic solid which correspond to extreme values of the energy density. In the general formulation of the problem, and assuming the strain field as given, a linear elastic orthotropic three-dimensional solid is considered and the stationarity conditions are obtained. Such a set of algebraic equations is then explicitly solved referring to the cubic case and the optimal orientations are found as well. It is also pointed out how such orientations depend both on a material parameter and on the strain field.

KEY WORDS: structural optimization, anisotropic elasticity, strain energy density, cubic symmetry.

Paper No. 13 RV1

de Buhan P., Taliercio A.

A HOMOGENIZATION APPROACH TO THE YIELD STRENGTH OF COMPOSITE MATERIALS Eur. J. Mech./A Solids, Vol. 10, No. 2, pp. 129-154, 1991.

Unlike most of the classical approaches which resort to phenomenological criteria for describing the u1timate behaviour of composite materials, the implementation of a homogenization procedure within the framework of the yield design theory makes it possible to construct such a criterion in a rigorous way. A general formu1ation of the macroscopic strength condition for fibre reinforced composite materials is thus derived from the sole knowledge of the strength properties of their constituents (matrix and fibres) and of their structural arrangement as well. Moreover, the possibility of failure taking place only between matrix and fibres can be easily accounted for through the introduction of a decohesion criterion which limits the normal tensile stress component acting upon the interfaces. As a final outcome, a closed form failure condition which involves only a few parameters, relating respectively to the strength properties of each individual component, is proposed for mode1ling multidirectional reinforced composites with any volume percentage of fibres. A first comparison between theoretical predictions and several experimental data concerning both uniaxial and biaxial tests carried out on composite specimens proves to be quite satisfactory. The approach presented here outlines a possible method for

8

designing composite structures against failure.

KEY WORDS: homogenization, limit analysis, fiber reinforced composite materials, macroscopic strength.

Paper No. 14 RV2

Poggi C., Taliercio A., Sacchi Landriani G.

PAVIA CIVIC TOWER: NUMERICAL SIMULATIONS FOR THE DETERMINATION OF THE STRESS STATE AND THE MECHANICAL PROPERTIES OF MASONRY (in Italian) TeMa - Tempo, Materia, Architettura, n. 3, pp. 46-55, 1993.

The results are presented of some numerical analyses carried out to determine the stress state in the Civic Tower of Pavia (Italy) induced by the self-weight and by wind effects. The mechanical properties of masonry were determined from experiments, supplemented by detailed numerical simulations. A reasonable hypothesis was formulated for the collapse of the Tower according to the computed stress state which was particularly high in some parts of the building.

KEY WORDS: Pavia Civic Tower, masonry, finite elements, creep failure.

Paper No. 15 CV1

Taliercio A., Rovati M., Sacchi Landriani G.

FORMULATION OF A MACROSCOPIC STRENGTH CRITERION FOR TRIDIRECTIONAL FIBER COMPOSITES in ‘Mechanics of composite materials at elevated and cryogenic temperatures’, S.N. Singhal, W.F. Jones, C.T. Herakovich & T. Cruse (Eds.), ASME, New York, pp. 171-180, 1991.

The theory of homogenization applied to limit analysis allows to rigorously define the macroscopic strength properties of periodic multi-phase materials, such as composite materials reinforced by arrays of equally spaced fibers, embedded in a matrix. By means of this approach, the strength properties of composite laminae reinforced by long and parallel fibers have already been obtained by various authors. The theoretical results established for these materials showed excellent agreement with experimental findings. The aim of the present work is to extend the same procedure to composites reinforced by a tridirectional array of mutually orthogonal fibers, which are materials of recent development. Through a static approach of limit analysis applied to a representative volume element, lower bounds to the actual failure domain of the material is obtained. This a1lows the numerical computation of strength domains for the material subjected to complex states of stress. Furthermore, if the material is subjected to uniaxial tension at any orientation to the fibers, analytical equations for the macroscopic strength are derived and discussed as well.

9

Finally, mention is made to the influence of the limited strength properties of the fiber-matrix interface upon the macroscopic strength of the composite.

KEY WORDS: homogenization, limit analysis, three-directional fiber reinforced composites, macroscopic strength.

Paper No. 16 CV1

Rovati M., Taliercio A., Cinquini C.

ON MAXIMUM STIFFNESS OF ORTHOTROPIC SHELLS in ‘Optimization of structural systems and industrial applications’, S. Hernandez & C.A. Brebbia (Eds.), Computational Mechanics Publications (Southampton-Boston) & Elsevier Appl. Sci. (London-New York), pp. 597-604, 1991.

Assuming the specific elastic strain energy as a meaningful measure of the stiffness/flexibility of a structural element, in this paper orthotropic shell structures of general shape will be considered and extreme values of the stored strain energy density sought. The role of design variable will be played by the local orientation of the principal directions of orthotropy with respect to a given reference frame, defined on the mid-surface of the shell. Assuming the strain field as prescribed, the optimization problem will be formulated in variational form as a min max problem and the necessary condition for stationarity will be obtained as well. Special features of such optimality condition will be discussed and the analogies with similar problems in plane elasticity pointed out.

KEY WORDS: structural optimization, anisotropic shells, strain energy density.

Paper No. 17 RV1

Cividini A., Taliercio A., Sacchi Landriani G., Bellotti R., Ferrara G., Rossi P.

AN APPARATUS FOR CYCLIC TRIAXIAL TESTS ON CYLINDRICAL CONCRETE SPECIMENS Materials & Structures, Vol. 25, pp. 490-498, 1992.

An apparatus specifìcally designed for static and cyclic testing of concrete and rock cylindrical samples is described. A particular characteristic of this equipment is the possibility of cyclic variation of the confining pressure, in addition to variation of the vertical load. The technical features of the apparatus are illustrated, as well as those of the instruments used for measuring and recording the variation of loads and displacements during the tests, up to the failure of the specimens. Comments are also presented on the devices controlling the variation of load with time and on the characteristics of the load histories adopted in an experimental research aimed at investigating the behaviour of concrete under repeated triaxial loads.

KEY WORDS: triaxial cell, cyclic loads, fatigue, concrete.

10

Paper No. 18 RV1

Taliercio A.

LOWER AND UPPER BOUNDS TO THE MACROSCOPIC STRENGTH DOMAIN OF A FIBER REINFORCED COMPOSITE MATERIAL Int. J. Plasticity, Vol. 8, No. 6, pp. 741-762, 1992.

The macroscopic strength domain of a composite material reinforced by long, parallel fibers is, in general, unknown but for its theoretical definition. In this note it is shown how a homogenization technique applied to yield design theory allows the derivation of two domains (in the space of macroscopic stresses) that are a lower and an upper bound to the composite strength domain. The dependence of these domains on the fiber content and on the shape of the fiber array is pointed out. Analytical equations for the approximate uniaxial macroscopic strength of composites with Drucker-Prager or Von Mises type matrix are derived. For more complex stress conditions, the relevant strength domains are numerically evaluated as well. The discrepancy between the two bounds is in many cases relatively small. In particular, the two bounds yield the same value for the uniaxial strength of the composite along the fiber direction, which, by consequence, is exactly determined.

KEY WORDS: fiber reinforced composites, homogenization, periodic media, macroscopic strength.

Paper No. 19 CV1

Poggi C., Taliercio A., Capsoni A.

FIBER ORIENTATION EFFECTS ON THE BUCKLING BEHAVIOUR OF IMPERFECT COMPOSITE CYLINDERS in ‘Buckling of Shell Structures on Land, in the Sea and in the Air’, J.F. Jullien (Ed.), Elsevier Pub. Ltd., London, pp. 114-123, 1991.

A theoretical and numerical investigation on the influence of the fibre orientation on the buckling behaviour of composite cylinders is presented. Composite cylinders with different laminations and subject to axial compression are examined. The results show the great influence of fibre orientation on the buckling load and highlight the presence of a high number of almost coincident buckling modes in the cases of quasi-isotropic lay- up or of a particular value of the fibre angle. In the latter case the initial slope of the post-buckling branch has a very high negative value and the cylinders consequently result to be very imperfection sensitive. This confirms the fact that any optimisation process should include an imperfection sensitivity parameter.

KEY WORDS: fiber reinforced composites, cylinders, buckling, imperfection sensitivity.

11

Paper No. 20 CV2

Taliercio A.

INFLUENCE OF THE FIBER-MATRIX INTERFACE IN THE FORMULATION OF MACROSCOPIC STRENGTH MODELS FOR COMPOSITE MATERIALS (in Italian) Proc. AIMETA Congress on ‘Mechanics of Materials and Structures’, Amalfi (I), June 3-5, 1991, pp. 315-324.

Aim of the work is the definition of domains apt to describe the overall strength properties of composite materials reinforced by long, parallel fibers, with a fiber-matrix interface of finite strength. To this end, a homogenization procedure for periodic media is employed in the framework of limit analysis theory, which allows one to define the macroscopic strength domain, Ghom, according to the known strength domains of the components (fiber, matrix and interface). By formulating suitable microscopic stress fields and failure mechanisms for a representative volume of the composite, inner and outer bounds to Ghom can be defined. Analytical expressions are also derived to approximate the composite strength under particular stress conditions in the case of matrix and interface complying with von Mises or Tresca yield conditions. Finally, further developments are outlined to improve the model and reduce the gap between the obtained bounds.

KEY WORDS: fiber reinforced composites, homogenization, periodic media, macroscopic strength, interface.

Paper No. 21 CV2

Papa E., Taliercio A.

A DAMAGE MODEL FOR CONCRETE APPLIED TO THE INTERPRETATION OF CYCLIC TESTS (in Italian) Proc. XI Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Trento (I), September 29-October 2, 1992, pp.443-448.

In the framework of damage mechanics, a model is presented for the description of the behaviour of concrete samples submitted to uni- and triaxial fatigue tests. This model is successfully applied to the interpretation of experimental results. The problem of identifying the model parameters is discussed. A first attempt to relating these parameters with the test conditions is made.

KEY WORDS: damage mechanics, cyclic tests, concrete.

Paper No. 22 CV2

Taliercio A., Rovati M.

EXTREME VALUES OF THE STRAIN ENERGY DENSITY FOR

12

TRANSVERSELY ISOTROPIC ELASTIC SOLIDS (IN ITALIAN) Proc. XI Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Trento (I), September 29-October 2, 1992, pp.493-499.

Dealt with is the problem of finding the orientations of the axis of symmetry of rotation which locally maximize (or minimize) the strain energy density in elastic, transversely isotropic, three-dimensional solids. Optimal solutions can be either ‘trivial’ i.e. featured by collinearity of material symmetry axes, principal stresses and principal strains, or ‘non-trivial’: the latter ones depend on parameters related both to the material elastic properties and to the principal strains. Orientations corresponding to extrema are analytically derived; the nature of these solutions is studied and absolute maxima (or minima) for the strain energy density are distinguished by other stationarity points.

KEY WORDS: anisotropic elasticity, strain energy density, transverse isotropy.

Paper No. 23 CV1

Papa E., Taliercio A.

A DAMAGE MODEL FOR TRIAXIAL FATIGUE OF CONCRETE: THEORETICAL FORMULATION AND PARAMETRIC INVESTIGATION Proc. Int. Seminar on Micromechanics of Materials “MECAMAT 93”, Moret-sur-Loing (F), 6-8/7/1993, pp. 543-554.

A theoretical model for the description of the behaviour of concrete submitted to uni- and triaxial fatigue tests has been developed. It is based on damage mechanics and can be seen as extension of models formulated by other authors for static or quasi-static load histories. Special attention is devoted to the influence of the parameters defining the damage evolution law on the material fatigue life. In particular, some of the parameters are found to play a negligible role, at least in the range of values usually encountered for concrete. In the case of triaxial tests on cylinders, the effect of lateral confinement is carefully examined. The results obtained are discussed and possible further improvements are foreseen. The presented model also gives indications about the type of experimental information needed to forecast the fatigue lire of concrete under general load histories.

KEY WORDS: damage, triaxial fatigue, concrete.

Paper No. 24 CV1

Rovati M., Taliercio A.

BOUNDS ON THE ELASTIC STRAIN ENERGY DENSITY IN 3-D BODIES WITH MATERIAL SYMMETRIES Proc. ‘Structural Optimization 93’, The World Congress on Optimal Design of Structural Systems, Rio de Janeiro, 2-6/8/1993, J. Herskovits (Ed.), pp. 353-360.

13

Dealt with is the determination of the orientation of the material symmetry axes at which a 3D body made of aleotropic materials exhibits the stiffest (or possibly, the most flexible) response. As a general rule, this is shown to require co1linearity of principal stresses and principal strains. The two cases of materials with cubic symmetry and transversely isotropic materials are studied in detail. For transversely isotropic materials, optimal solutions can be either ‘trivial’, i.e. featured by full col1inearity of material symmetry axes and principal strains. or ‘quasi-trivial’, where collinearity is only partial1y preserved. For materials with cubic symmetry. possible are also ‘non-trivial’ solutions. featured by equal axial strains along the three symmetry axes. Optimal orientations are analytically derived and the relevant solutions classified: of great importance to this end is a parameter depending only on the elastic material properties.

KEY WORDS: structural optimization, anisotropic elasticity, strain energy density, cubic symmetry, transverse isotropy.

Paper No. 25 CL1

Taliercio A.

APPLICATION OF HOMOGENIZATION THEORY AND LIMIT ANALYSIS TO THE EVALUATION OF THE MACROSCOPIC STRENGTH PROPERTIES OF FIBER REINFORCED COMPOSITE MATERIALS in ‘Evaluation of global bearing capacities of structures’, G. Sacchi Landriani & J. Salençon (Eds.), Springer-Verlag, Wien, pp. 91-120, 1993.

The macroscopic strength domain of a composite material reinforced by long, parallel fibers is, in general, unknown but for its theoretical definition. In this note it is shown how a homogenization technique applied to yield design theory allows the derivation of two domains (in the space of macroscopic stresses) which are a lower and an upper bound to the composite strength domain. The dependence of these domains on the fìber content and on the shape of the fìber array is pointed out. Analytical equations for the approximate uniaxia1 macroscopic strength of composites with Drucker-Prager or Von Mises type matrix are derived. For more complex stress conditions, the relevant strength domains are numerica1ly evaluated as well. The discrepancy between the two bounds is in many cases relatively sma1l. In particular, the two bounds yield the same value for the uniaxial strength of the composite along the fìber direction, which by consequence is exactly determined.

KEY WORDS: fiber reinforced composites, homogenization, periodic media, macroscopic strength.

Paper No. 26 RV1

Taliercio A., Sagramoso P.

UNIAXIAL STRENGTH OF POLYMERIC-MATRIX FIBROUS COMPOSITES

14

PREDICTED THROUGH A HOMOGENIZATION APPROACH Int. J. Solids Structures, Vol. 32, No. 14, pp. 2095-2123, 1995.

A homogenization technique applied in conjunction with limit analysis theory allows the prediction of the macroscopic strength of fiber composites as a function of the strength properties of the phases (i.e. fiber, matrix and interface). Emphasis is placed here on the uniaxial strength, for which bounds based on static and kinematic approaches are proposed. Special attention is devoted to the influence of the matrix, which is presumed to be polymeric and complying with Drucker-Prager, Mohr-Coulomb or a parabolic type criterion. Also the limited strength of the fiber-matrix interface is accounted for through the introduction of a Mohr-Coulomb type strength criterion. Analytical equations describing the dependence of the macroscopic strength of the composite on the orientation of the applied stress with respect to the fibers are proposed. The parameters required to define the model are limited in number and possess a clear mechanical meaning. Comparisons with experimental data available in the literature prove quite satisfactory.

KEY WORDS: homogenization, limit analysis, macroscopic strength, off-axis strength, interface.

Paper No. 27 CV1

Sacchi Landriani G., Taliercio A.

ON THE OPTIMAL DESIGN OF BODIES WITH MATERIAL SYMMETRIES in ‘Advances in Design Automation’, B.J. Gilmore, D.A. Höltzl, D. Dutta & H.A. Eschenauer (Eds.), ASME, pp. 225-235, 1994.

The paper is concerned with the optimal design of two dimensional, in-plane loaded structural elements and three dimensional bodies, made of aleotropic materials, with regard to both the elastic and the ultimate behaviour. Sec. 2 is devoted to finding the local orientations of the material symmetry axes in 3D orthotropic solids, corresponding to extreme values of the global elastic stiffness. These orientations are shown to be such that collinearity of principal stress and principal strains is achieved throughout the body. In the particular case of transversely isotropic or cubic materials, optimal orientations are shown to depend both on a material parameter and the strain field. A certain orientation of the material symmetry axes may correspond either to a minimum or to a maximum in the elastic stiffness, depending on whether the material has ‘high’ or ‘low shear modulus’. These results are then specialized to plane orthotropic bodies, in which case the theoretical findings obtained by other authors are recovered. In the plane case, also simultaneous optimization of fiber orientation and density is dealt with. Sec. 3 concerns optimal limit design of plastic 2D in-plane loaded orthotropic structures. Fiber orientation and density are assumed as design variables. Here again, necessary optimality conditions are analytically found and their mechanical interpretation is studied. Analogies with both the numerical results of other authors and the elastic case are observed and discussed

15

as well.

KEY WORDS: structural optimization, anisotropic elasticity, strain energy density, limit analysis, 2D solids.

Paper No. 28 CL1

Sacchi Landriani G., Rovati M., Taliercio A.

MATERIAL ANISOTROPY AND WORK STRAIN CHARACTERIZED BY STATIONARY VALUES OF STRAIN ENERGY DENSITY FUNCTION in ‘Advanced Technology for Design and Fabrication of Composite Materials’, G.C. Sih, A. Carpinteri & G. Surace (Eds.), Kluwer Acad. Pub., pp. 85-100, 1995.

Stationary values of the strain energy density function are used to determine the relative position of the material symmetry axes and those of principal stress and strain. The minima and maxima would determine the directions of orthotropy for which the body would exhibit the stiffest or softest response. Variational principle is applied to formulate the orthotropic linear elastic problem in three dimensions. Solutions are obtained for a cubic and transversely isotropic material such that the principal axes of stress and strain are aligned with the axes of orthotropy according to the stationary values of the strain energy density. Similar considerations are given to the plane state of stress where the variational process would also involve the material coefficients as independent variables.

KEY WORDS: structural optimization, anisotropic elasticity, strain energy density, 2D solids.

Paper No. 29 CV2

Papa E., Taliercio A.

AN ANISOTROPIC DAMAGE MODEL FOR CONCRETE SUBJECTED TO MULTIAXIAL CYCLIC LOADS: THEORETICAL FORMULATION AND EXPERIMENTAL VALIDATION (in Italian) Proc. XII Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Napoli (I), October 3-6, 1995, Vol. V, pp.141-146.

An anisotropic damage model for concrete is proposed which is capable of describing the material behaviour both under static and cyclic uni- and triaxial load histories. The model is featured by two independent damage tensors which separately account for damage induced by tensile or compressive strains. This proposal is furtherly extended to simulate cumulation of damage and permanent strains during fatigue tests. Comparison between model response and available experimental results is encouraging. Finally, possible future extensions are outlined.

KEY WORDS: damage, anisotropy, concrete, multiaxial fatigue.

16

Paper No. 30 RV1

Taliercio A., Gobbi E.

EXPERIMENTAL INVESTIGATION ON THE TRIAXIAL FATIGUE BEHAVIOUR OF PLAIN CONCRETE Mag. Concr. Res., Vol. 48, No. 176, pp. 157-172, 1996.

An experimental research program was carried out with the aim of investigating the effects of a cyclic triaxial loading upon the mechanical behaviour of concrete. A triaxial press was used, capable of applying on cylindrical specimens an axial load and a confining pressure cyclically varying in time according to independent programs. Cycles (at 1 Hz) were characterized by different (a) mean stress, (b) amplitude, (c) ratio r of the mean confining pressure to the mean axial stress and (d) phase angle between loads. Some uniaxial cyclic tests were also performed. Those specimens that did not fail within about 400,000 cycles were monotonically tested to failure in uniaxial compression. Despite their scatter, the obtained results qualitatively show that: (a) at equal other tests parameters, fatigue life is usually shorter in tests in phase opposition rather than in phase coincidence; (b) as the cycle amplitude increases, fatigue life decreases (mainly in tests in phase opposition); (c) fatigue life increases as the mean confinement increases; (d) a strong correlation exists between 'secondary creep rate' and fatigue life, irrespective of the ratio between mean stresses; (e) all specimens submitted to post-cyclic failure tests exhibited a decrease in elastic modulus as greater as higher r was during cycles; the specimens submitted to uniaxial cycles experienced an increased in static strength in comparison with the virgin ones.

KEY WORDS: plain concrete, triaxial fatigue, cyclic creep, Wöhler's diagrams.

Paper No. 31 RV1

Papa E., Taliercio A.

ANISOTROPIC DAMAGE MODEL FOR THE MULTIAXIAL STATIC AND FATIGUE BEHAVIOUR OF PLAIN CONCRETE Engng Frac. Mech., Vol. 55, No. 2, pp. 163-179, 1996.

A theoretical model is proposed for the description of the static and fatigue behaviour of plain concrete under uni- and triaxial loading. The model is based on damage mechanics: it features two second-order symmetric damage tensors, representative of surface damage induced by tensile or compressive strains, and a scalar variable representative of volumetric damage. Assuming independence of tensile and compressive damage variables also allows accounting for crack-closure effects. A thermodynamically consistent damage evolution law is proposed. Permanent strains upon unloading are related to damage through empirical equations. The model can cover cyclic loading inducing fatigue by means of a simple extension requiring only one additional parameter to be

17

determined. A possible strategy for the identification of the model parameters from experiments is outlined. The reliability of the model is assessed through comparison with results of static and cyclic tests.

KEY WORDS: plain concrete, triaxial stress, damage mechanics, anisotropy.

Paper No. 32 RV1

Papa E., Taliercio A., Gobbi E.

TRIAXIAL CREEP BEHAVIOUR OF PLAIN CONCRETE AT HIGH STRESSES: A SURVEY OF THEORETICAL MODELS Materials & Structures, Vol. 31, pp. 487-493, 1998.

A survey was performed to find in the literature theoretical models suitable to the description of the triaxial creep behaviour of plain concrete at high stresses. The considered models are based on the theory of elasto-viscoplasticity with damage and are mainly addressed to the domain of geotechnics. Application of these models to the simulation of experiments turned out to be satisfactory on the whole, although several features of the creep behaviour of the material are not reproduced. The suggestions given by this preliminary work will be taken into account in the development of a future model specifically conceived for concrete.

KEY WORDS: plain concrete, creep, damage, viscoplasticity.

Paper No. 33 RV1

Pandolfi A., Taliercio A.

BOUNDING SURFACE MODELS APPLIED TO FATIGUE OF PLAIN CONCRETE Journal of Engineering Mechanics, ASCE, Vol. 124, No. 5, pp. 556-564, 1998.

A survey was performed to find in the literature theoretical models capable of describing the fatigue behaviour of concrete, subjected to uni- and triaxial elevated stress. Four models were selected, which are based on the concept of «bounding surface». Several numerical simulations of fatigue tests were performed to assess the potentiality of these models in the domain of fatigue. Whereas the response of two of these models is consistent with the loading conditions in most simulations, the other ones are unable to take the effect of confining pressure into account. All of the models, however, require modifications to give realistic predictions of fatigue life and cyclic creep. The parameters that mostly seem to affect the model response under fatigue are devised and slightly modified; comparisons with available experimental data support the validity of this proposal. This preliminary research is intended to be the first step toward the incorporation of rate effects into the models considered, or other theoretical models.

18

KEY WORDS: plain concrete, fatigue, damage, cyclic creep, bounding surface, loading surface, plasticity, permanent strain.

Paper No. 34 RV1

Taliercio A., Gobbi E.

EFFECT OF ELEVATED TRIAXIAL CYCLIC AND CONSTANT LOADS ON THE MECHANICAL PROPERTIES OF PLAIN CONCRETE Magazine of Concrete Research, Vol. 49, No. 181, 1997, pp. 353-365.

An experimental programme was carried out to investigate the effect of elevated cyclic or constant triaxial stresses on the change in mechanical properties of plain concrete. Triaxial cyclic tests on cylinders, with confining pressure and axial load varying in phase opposition at 1 Hz, were performed in three different deviatoric planes. The maximum stress deviator was 90% of the deviator at failure in a given deviatoric plane; the minimum deviator was 80% of the maximum one. In constant-load tests, the applied stresses were equal to the stresses at the maximum deviator applied in cyclic tests. At the cycle amplitudes selected, the creep effects under constant load are usually larger than the dynamic effects. The results obtained show that: the residual strength is increased with respect to the strength of companion virgin specimens, for any test condition; the increase in residual strength is much more important in triaxial tests than in uniaxial tests and increases with the test duration; the decrease in elastic modulus increases with the isotropic pressure at which tests are performed; and the test duration has a less pronounced effect on the decrease in elastic modulus.

KEY WORDS: plain concrete, triaxial fatigue, triaxial creep, residual strength, damage.

Paper No. 35 RV1

Taliercio A., Gobbi E.

FATIGUE LIFE AND CHANGE IN MECHANICAL PROPERTIES OF PLAIN CONCRETE UNDER TRIAXIAL DEVIATORIC CYCLIC STRESSES Magazine of Concrete Research, Vol. 50, No. 3, pp. 247-255, 1998.

The effects of a lateral confinement on the fatigue behaviour of plain concrete are experimentally investigated. Triaxial cyclic tests on cylinders, with confining pressure and axial load varying in phase opposition at 1 Hz, were performed in different deviatoric planes. The maximum stress deviator was 90% of the deviator at failure in a given deviatoric plane; the minimum deviator ranged between 70% and 95% of the maximum one. The residual strength and stiffness properties of those specimens that did not fail within a prescribed number of cycles were also assessed. For tests with cycles of equal amplitude (normalized to the triaxial static strength), fatigue life and residual strength seem to be

19

positively affected by an increase in hydrostatic stress only up to a certain level. With the maximum deviator equal, in a given deviatoric plane fatigue life usually increases with decreasing cycle amplitude. In one of the deviatoric planes, cycle amplitude and mean stress were found to have opposite effects upon damage and residual strength.

KEY WORDS: plain concrete, triaxial fatigue, fatigue life, residual strength, damage.

Paper No. 36 RV1

Taliercio A., Coruzzi R.

MECHANICAL BEHAVIOUR OF BRITTLE MATRIX COMPOSITES: A HOMOGENIZATION APPROACH International Journal of Solids and Structures, Vol. 36, No. 24, pp. 3591-3615, 1999.

A numerical model is developed with the aim of describing the macroscopic mechanical response of unidirectional brittle-matrix fiber-reinforced composites subjected to stresses acting in any plane transverse to the fibers. Finite element analyses of a representative unit cell are performed, with suitable boundary conditions ensuring continuity of the displacement field across adjacent cells and periodicity of the strain field over the cell. A strain-softening constitutive law is adopted for the matrix in tension to allow, for instance, for brittleness induced by possible defects in a polymeric matrix. The perfectly plastic case is also considered for sake of comparison. Results established for ductile composites are found to be inappropriate for brittle matrix composites: numerical analyses show that composites with softening matrix have transverse strength properties much poorer than perfectly plastic composites with matrix of equal strength, and even than the unreinforced matrix. An induced transverse anisotropy in the post-peak regime is also observed. A discussion on the proposed approach concludes the note.

KEY WORDS: composites, homogenization, finite elements, brittle matrix, smeared crack.

Paper No. 37 CV2

Taliercio A.

HOMOGENIZATION OF FIBER-REINFORCED COMPOSITES WITH ELASTOPLASTIC MATRIX (in Italian) Proc. XIII Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Siena (I), September 29-October 3, 1997, Vol. III, pp. 1-6.

A numerical model was developed for the evolutive analysis of unidirectional fiber composites. The model is based on homogenization theory for periodic media and requires a single representative volume element (RVE) to be analyzed. The related structural problem is numerically solved by the finite

20

element method. Particular attention is given to the boundary conditions that ensure the continuity of the displacement field across adjacent RVEs and the periodicity of the microscopic strain field. The results obtained for metal composites are compared with the findings of other authors: the importance of a correct enforcement of the boundary conditions to reliably estimate the macroscopic response is emphasized. For perfectly plastic composites, the numerical results agree with previously obtained theoretical predictions as far as the ultimate strength is concerned.

KEY WORDS: composites, homogenization, elastoplastic matrix.

Paper No. 38 CV2

Papa E., Taliercio A.

A VISCOPLASTIC MODEL WITH DAMAGE FOR CONCRETE SUBJECTED TO SUSTAINED ELEVATED STRESSES (in Italian) Proc. XIII Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Siena (I), September 29-October 3, 1997, Vol. III, pp. 13-18.

A viscoplastic model with damage was developed to describe the mechanical behaviour of plain concrete subjected to sustained multiaxial stresses of high intensity. The model is characterized by inelastic strains due to plasticity and damage and by a second-order damage tensor. The evolution laws for these variables are based on the proposals by other authors for metals and rocksalt. The reliability of the model, presented here in the uniaxial case, was assessed through comparisons with available test results.

KEY WORDS: plain concrete, creep, damage, viscoplasticity.

Paper No. 39 CL1

Papa E., Taliercio A.

ANISOTROPIC DAMAGE MODEL FOR THE TRIAXIAL CREEP BEHAVIOUR OF CONCRETE in ‘Damage Mechanics in Engineering Materials’, G.Z. Voyiadjis, J.-W. Ju & J.-L. Chaboche (Eds.), Elsevier Sci. B.V., 1998, pp. 337-350.

A viscoplastic model with damage was developed to describe the mechanical behaviour of plain concrete subjected to sustained multiaxial stresses of high intensity. The model is characterized by inelastic strains due to plasticity and damage, and by a second-order damage tensor. The evolution laws for these variables are formulated by extending the proposals of other authors for metals and rocksalt. The procedure to obtain the main model parameters from experiments is also outlined. The reliability of the model was assessed through comparisons with available test results.

21

KEY WORDS: plain concrete, creep, damage, viscoplasticity.

Paper No. 40 CV1

Frassine R., Taliercio A.

VISCOELASTIC BEHAVIOUR OF POLYMER-MATRIX COMPOSITES: NUMERICAL MODELING AND EXPERIMENTAL VALIDATION Proc. 4th Int. Conf. on Composites Engineering - ICCE/4, Kona Big Island, USA, July 6-11, 1997, pp. 331-332.

The transverse mechanical behaviour of continuous fiber reinforced materials is of paramount importance in predicting the overall behaviour of complex structures. The analysis of the stress state in mechanically fastened joints, for example, cannot simply be restricted to the fiber plane. Due to the viscoelastic nature of the matrix, polymer-based composites usually exhibit significant time-dependent behaviour in the transverse direction. Even under constant external loading, this leads in time to stress redistribution around the fibers. In the present work, the linear viscoelastic behaviour of a glass-fiber/polyester pultruded composite was studied both numerically and experimentally. A time-dependent damage model is also proposed for the fiber-matrix interface.

KEY WORDS: polymer-matrix composites, laboratory testing, viscoelasticity, damage, homogenization, finite elements.

Paper No. 41 CV2

Poggi C., Taliercio A.

EXPERIMENTAL ANALYSIS AND MICROMECHANICAL MODELLING OF LAMINATED GLASS-FIBER FABRICS (in Italian) Proc. FAST Congress ‘Materiali - Ricerca e prospettive tecnologiche alle soglie del 2000’, Milano, November 10-14, 1997, Vol. 2, pp. 927-934.

The paper illustrates the results of a theoretical-experimental research covering the mechanical behaviour of glass-fiber fabrics. Owing to the complex geometry of the reinforcement, the different properties of warp and weft, and the frequently observed nonlinear response, these materials need to be carefully characterized in order to fully exploit their mechanical properties. Particular attention was given in the experimental activities to the sources of nonlinearity, to define a limit stress for design purposes. During tension tests, a testing device was employed to monitor the acoustic emissions that accompany local fiber failures often responsible for the nonlinear response. This allowed the identification of the position and the number of microfractures in the specimens at different load levels and the correlation of the final failure to the localization of the microfractures. A finite element numerical model was also developed to describe the global (or ‘macroscopic’) response of the fabric under any loading condition. The model takes a single 3D ‘Representative Volume Element’ (RVE)

22

of fabric into account. By imposing suitable displacement conditions at the boundary of the RVE, the macroscopic properties of the composite can be predicted based on the properties of the components and the geometry of the reinforcement.

KEY WORDS: fabrics, glass-fibers, testing, acoustic emission, homogenization.

Paper No. 42 CV1

Carvelli V., Maier G., Taliercio A.

LIMIT ANALYSIS OF PERIODIC COMPOSITES BY A KINEMATIC APPROACH Proc. 8th European Conference on Composite Materials - Science, Technology and Applications (ECCM-8), Napoli, June 3-6, 1998, Vol. 4, pp. 389-396.

The efficient evaluation of strength domains for metal-matrix composite (MMC) materials with unidirectional periodic fibers is the objective pursued in this paper. The analyses presented are based on the kinematic limit theorem and on the finite element method in its displacement formulation. The resulting nonlinear mathematical programming problems are solved by an iterative procedure. The limit analysis method developed and implemented for MMCs takes the strain-periodicity of the microscopic displacement field into account and directly leads to an upper bound of the collapse multiplier and to a collapse mechanism. The numerical tests performed so far exhibit fast convergence and show excellent agreement with experimental and numerical results arising from different approaches.

KEY WORDS: limit analysis, periodic composites, homogenization, finite elements.

Paper No. 43 CV2

Carvelli V., Maier G., Taliercio A.

LIMIT AND SHAKEDOWN ANALYSIS OF PERIODIC COMPOSITES Proc. XI Italian Computational Mechanics Conference (GIMC 98), Trento, July 13-15, 1998, pp. 71-74.

The objective of this paper is to present a computationally cost effective approach to limit and shakedown analysis of metal-matrix composite materials. The analyses presented are based on: the homogenization theory for periodic media, the kinematic limit and shakedown theorems and the finite element method in its displacement formulation. The resulting nonlinear mathematical programming problems are solved by an iterative procedure. The numerical tests performed so far exhibit fast convergence and show excellent agreement with numerical results arising from different approaches.

KEY WORDS: limit analysis, shakedown, periodic composites, homogenization, finite elements.

23

Paper No. 44 RV2

Carvelli V., Maier G., Taliercio A.

SHAKEDOWN ANALYSIS OF PERIODIC HETEROGENEOUS MATERIALS BY A KINEMATIC APPROACH Strojnícky Casopis (Mechanical Engineering), Vol. 50, No. 4, pp. 229-240, 1999.

A kinematic approach to shakedown analysis of periodic heterogeneous media is presented in the framework of the homogenization theory. The evaluation of the “macroscopic” shakedown limit for a given domain of variable repeated average stresses is computed by an iterative procedure which solves a mathematical programming problem formulated on a Representative Volume (RV) with periodicity boundary conditions.

KEY WORDS: shakedown, heterogeneous materials, composites, homogenization, finite element method.

see also:

Carvelli V., Maier G., Taliercio A.

NUMERICAL SHAKEDOWN ANALYSIS OF PERIODIC HETEROGENEOUS MATERIALS BY A KINEMATIC APPROACH Proc. VII Int. Conf. on Numerical Methods in Continuum Mechanics (NMCM ‘98), High-Tatra (SLK), October 6-9, 1998, pp. 271-276.

Paper No. 45 RV1

Carvelli V., Taliercio A.

A MICROMECHANICAL MODEL FOR THE ANALYSIS OF UNIDIRECTIONAL ELASTOPLASTIC COMPOSITES SUBJECTED TO 3D STRESSES Mechanics Research Communications, Vol. 26, No. 5, pp. 547-553, 1999.

A numerical model is presented to predict the global (or macroscopic) response of fiber-reinforced composites subjected to any stress condition. The reinforcing array is supposed to be of regular geometry, so that the model can be developed within the framework of the micromechanical theory for periodic heterogeneous media. Special attention is devoted to correctly imposing the kinematic boundary condition that have to be fulfilled by the microscopic displacement field. The reliability of the model is checked through comparisons with the numerical results of other authors.

KEY WORDS: composites, homogenization, plasticity, finite elements.

see also:

Taliercio A., Carvelli V.

24

MICROMECHANICAL MODEL FOR THE ANALYSIS OF ELASTOPLASTIC UNIDIRECTIONAL COMPOSITES SUBJECTED TO 3D STRESSES (in Italian) Proc. XI Italian Computational Mechanics Conference (GIMC 98), Trento, July 13-15, 1998, pp. 153-156.

Paper No. 46 CV1

Taliercio A., Carvelli V.

2D FINITE ELEMENTS FOR THE ANALYSIS OF FIBER REINFORCED COMPOSITES SUBJECTED TO 3D STRESSES Proc. 9th European Conference on Composite Materials - Science, Technology and Applications (ECCM-9), München (D), August 30-September 3, 1999 (CD ROM).

A numerical model suitable for the prediction of the overall mechanical response of unidirectional fiber reinforced composites (FRCs) under any macroscopic stress condition has been developed. This model consists of a mesh of plane finite elements, with particular boundary conditions that account for the periodicity of the reinforcing array. The finite elements have been expressly developed to describe particular 3D microscopic displacement fields, associated with strain fields that do not vary along the fiber axis. Elements with the above features have been implemented in a commercial finite element code and employed to analyze elastic FRCs under general 3D stresses. The effectiveness of the proposed elements has been checked though comparisons with available experimental and theoretical results regarding the macroscopic thermoelastic properties of different FRCs. The model turns out to be definitely advantageous in comparison with fully 3D finite element models in terms of allocated memory and number of constraints to be accounted for to enforce the boundary conditions periodicity.

KEY WORDS: composites, homogenization, generalized plane strain, finite elements.

Paper No. 47 RV1

Taliercio A., Berra M., Pandolfi A.

EFFECT OF HIGH-INTENSITY SUSTAINED TRIAXIAL STRESSES ON THE MECHANICAL PROPERTIES OF PLAIN CONCRETE Magazine of Concrete Research, Vol. 51, No. 6, pp. 437-447, 1999.

An experimental research program was carried out to investigate the effects of high-intensity prolonged triaxial stresses on the strength and stiffness properties of concrete. The tested specimens were subjected to constant stresses equal to 90-95% of the failure stress deviator under monotonic loading in different deviatoric planes. The stiffness properties of the specimens were evaluated at different time intervals. The decrease in shear modulus was taken as a measure of the creep-induced damage. The specimens that did not fail at constant stress within five days were unloaded and monotonically reloaded to failure. For the

25

specimens tested at the lower stress, damage tends to stabilize after the early stage at constant load, whereas for the tests performed at the higher stress damage seems to keep on increasing for the entire duration of the creep test. The strength of the specimens survived to the creep tests was found to moderately increase with respect to the control samples, with the failure envelope of the material being dependent upon the hydrostatic creep stress.

KEY WORDS: plain concrete, experimental tests, damage, triaxial creep, residual strength.

Paper No. 48 CV2

Carvelli V., Taliercio A.

PLANE-STRAIN LIMIT ANALYSIS OF PERIODIC FIBER-REINFORCED COMPOSITES (in Italian) Proc. XIV Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Como (I), October 6-9, 1999 (CD ROM).

A numerical model was developed to predict the macroscopic strength of metal matrix composites reinforced by long parallel fibers. The model is based on the application of the kinematic approach of classical limit analysis to homogenization theory for periodic media. The collapse factor for any macroscopic stress acting in a plane transverse to the fibers is computed through an iterative process that reduces the relevant stationarity problem of a nonlinear functional to a sequence of linear problems. The functional is discretized by finite elements that accommodate incompatible (or ‘enhanced’) strain rates, thus avoiding ‘locking’ problems associated with the incompressibility constraint for plastic strains in plane strain conditions. The advantages of the proposed model are illustrated by comparisons with the results of other authors and those of incremental analyses with usual compatible elements.

KEY WORDS: composites, homogenization, limit analysis, plane strain, finite elements, locking, enhanced strain.

Paper No. 49 CV1

Carvelli V., Maier G., Taliercio A.

KINEMATIC LIMIT ANALYSIS OF PERIODIC HETEROGENEOUS MEDIA Computer Modeling in Engineering and Science, Vol. 1, No. 2, pp. 19-30, 2000.

Homogenization of periodic fiber-reinforced ductile composite materials is performed as for the material strength, i.e. the carrying capacity with respect to macroscopic (average) stresses. Rigid-plastic limit analysis is formulated by the kinematic theorem applied to the representative volume with periodicity boundary conditions and von Mises yield criterion. The iterative procedure adopted for the numerical solution of the minimization problem is comparatively

26

discussed on the basis of applications to various ductile heterogeneous media.

KEY WORDS: limit analysis, composites, periodic materials.

Paper No. 50 CV1

Papa E., Taliercio A.

PREDICTION OF THE EVOLUTION OF DAMAGE IN ANCIENT MASONRY TOWERS Proc. IASS-MSU Int. Symp ‘Bridging Large Spans from Antiquity to the Present’, Istanbul, May 29-June 2, 2000, pp. 135-144.

In this work, the results of numerical analyses carried out on a masonry tower are presented, with the aim of investigating the effects of creep-induced damage on the evolution of the global behaviour of the structure in time. These analyses were performed by implementing, into a commercial finite element code with user-oriented interface, a damage model recently developed by the authors to predict the creep behaviour of rock-like materials under constant stress and up to failure. The basic idea of this model is to describe primary creep through the Kelvin element of the Burger's rheological model, whereas the Maxwell's element consists of a spring and a dashpot in series where damage effects take place. The decrease in strength and stiffness associated with the occurrence of damage induces a stress redistribution throughout the structure. The numerical results show that the predicted zones of damage localization match the estimated failure mechanism of the tower, according to the morphology of the ruins.

KEY WORDS: masonry, damage, creep failure, rheological models, sustained loading, finite elements.

Paper No. 51 CV1

Papa E., Taliercio A., Mirabella-Roberti G.

A DAMAGE MODEL TO PREDICT THE BEHAVIOUR OF MASONRY UNDER SUSTAINED LOADING Proc. 12th International Brick/Block Masonry Conference (IB2MAC), Madrid, June 25-28, 2000, Vol. III, pp. 1777-1790.

The results of uniaxial creep tests to failure on rubble masonry samples are presented. These tests are meant to be representative of the stress conditions that may be responsible for the collapse of massive masonry structures. A theoretical damage model is proposed to simulate the experimental results. It is based on the theory of viscoelasticity coupled with two anisotropic damage variables, allowing, respectively, for damage induced by monotonically increasing stresses and by sustained stresses. The numerical simulations performed so far are quite encouraging, so that the applicability of the proposed model to structural analyses can be envisaged.

27

KEY WORDS: masonry, experimental tests, damage, creep, rheological models, sustained loading.

Paper No. 52 CL1

Maier G., Carvelli V., Taliercio A.

LIMIT AND SHAKEDOWN ANALYSIS OF PERIODIC HETEROGENEOUS MEDIA in ‘Handbook of Materials Behavior Models‘, J. Lemaitre (Ed.), Academic Press, San Diego (USA), 2001, Sec. 10.8, pp. 1025-1036.

The paper deals with heterogeneous media with periodic arrangement of the inclusions (fiber-reinforced composites, perforated plates) and ductile components, subjected to either monotonic or variable repeated loading. The fundamentals of the theoretical static and kinematic approaches to the determination of the macroscopic yield strength of the equivalent homogenized material are reviewed. Outlined are also numerical methods that give lower and upper bounds for the collapse multiplier of the representative volume (RV) based on linear or nonlinear programming. Then such methods are extended so as to cover the case of the shakedown analysis of RVs subjected to macroscopic stresses varying within a given domain. Numerical examples prove the effectiveness of the proposed algorithms through comparisons with both analytical and experimental available results.

KEY WORDS: limit analysis, shakedown analysis, heterogeneous periodic materials, linear and nonlinear mathematical programming.

Paper No. 53 CV1

Papa E., Taliercio A., Binda L.

CREEP FAILURE OF ANCIENT MASONRY: EXPERIMENTAL INVESTIGATION AND NUMERICAL MODELING in ‘Structural Studies, Repairs and Maintenance of Historical Buildings VII’, C.A. Brebbia (Ed.), WIT Press, Southampton (GB), 2001, pp. 285-294.

The recent collapse of some ancient massive buildings has raised attention on the creep behaviour of masonry. An extensive experimental and theoretical research program is being carried out on this topic at the Politecnico of Milan. The results are presented of accelerated creep tests to failure on brick masonry samples taken from a building (the Cathedral of Monza, Italy) that shows signs of serious damage. Then, a recently developed theoretical model is proposed to simulate the experimental results. It is based on the theory of viscoelasticity coupled with two anisotropic damage variables, allowing, respectively, for damage induced by monotonically increasing stresses and by sustained stresses. The numerical simulations performed so far are quite encouraging, so that the applicability of the proposed model to structural analyses can be envisaged.

28

KEY WORDS: masonry, experimental tests, damage, creep, rheological models, sustained loading.

Paper No. 54 CV1

Papa E., Taliercio A., Binda L.

SAFETY ASSESSMENT OF ANCIENT MASONRY TOWERS Proc. 2nd Int. Congress ‘Studies in Ancient Structures’ (SAS2001), G. Arun & N. Seçkin (Eds.), Istanbul, July 9-13, 2001, Vol. 1, pp. 345-354.

The results of structural analyses, carried out to assess the safety of a medieval masonry tower (the belltower of the Cathedral of Monza, Italy), are presented. The analyses were performed by means of a commercial finite element code with user-oriented interface. The interface was utilized to incorporate in the code a theoretical model, expressly developed to describe the creep behaviour of masonry up to failure, accounting for the evolution of damage. The reliability of this model was assessed in previous works, in which a masonry tower recently collapsed in Pavia (Italy) was analyzed and the predicted time to failure turned out to be close to the real one. The values of the parameters that define the model were obtained from experimental tests carried out on specimens taken from a part of the Cathedral contemporary to the tower. The numerical analyses point out the dangerousness of the tower conditions: indeed, a time to failure of about two centuries starting from today is predicted.

KEY WORDS: masonry, damage, creep failure, rheological models, sustained loading, finite elements.

Paper No. 55 CL2

Anzani A., Binda L., Papa E., Taliercio A.

MODELING OF THE TIME EVOLUTION OF DAMAGE IN ANCIENT MASSIVE MASONRY BUILDINGS (in Italian) in ‘Il Progetto di Conservazione: linee metodologiche per le analisi preliminari, l’intervento, il controllo di efficacia’, S. Pesenti (Ed.), Alinea, par. 2.5, pp. 151-163, 2001.

The failure of some ancient masonry buildings (e.g., the Civic Tower of Pavia, Italy) can be attributed to creep strains induced by the stresses acting in the structure. If compared to the short-term strength of the material, the intensity of these stresses may be such that the building is not deemed to be unsafe. Nevertheless, because of their persistence in time, they can induce an evolution of mechanical damage (in the form of microcracks) associated to a local decrease in strength, stiffness, etc. This paper synthesizes the results of a research program carried out in the last years on the safety of ancient masonry structures and the relevant interventions. First, a theoretical model developed by the authors is presented, suitable to predict the mechanical response of rubble

29

masonry under sustained loading and up to failure. Then, the model is calibrated according to experimental tests on specimens taken from the ruins of the Civic Tower of Pavia. After implementation in a commercial finite element code for nonlinear analyses, the model is applied to the structural analysis of the Tower. Special attention is paid to the time evolution of damage and the consequent prediction of the time to failure of the building. Finally, the guidelines are outlined which should be followed when operating on damaged masonry buildings, according to the information provided by the proposed model.

KEY WORDS: masonry, damage, rheological model, viscoelasticity, creep, failure.

Paper No. 56 RV1

Rovati M., Taliercio A.

STATIONARITY OF STRAIN ENERGY DENSITY FOR SOME CLASSES OF ANISOTROPIC SOLIDS Int. J. Solids Structures, Vol. 40, No. 22, pp. 6043-6075, 2003.

Homogeneous, anisotropic and linearly elastic solids, subjected to a given state of strain (or stress), are considered. The problem dealt with consists in finding the mutual orientations of the principal directions of strain to the material symmetry axes in order to make the strain energy density stationary. Such relative orientations are described through three Euler's angles. When the stationarity problem is formulated for the generally anisotropic solid, it is shown that the necessary condition for stationarity demands for coaxiality of the stress and the strain tensors. From this feature, a procedure which leads to closed form solutions is proposed. To this end, tetragonal and cubic symmetry classes, together with transverse isotropy, are carefully dealt with, and for each case all the sets of Euler's angles corresponding to critical points of the energy density are found and discussed. For these symmetries, three material parameters are then defined, which play a crucial role in ordering the energy values corresponding to each solution.

KEY WORDS: anisotropic elasticity, strain energy density, tetragonal symmetry, transverse isotropy, cubic symmetry.

Paper No. 57 CV1

Rovati M., Taliercio A.

A GENERAL APPROACH FOR THE EVALUATION OF STRAIN ENERGY EXTREMA IN ANISOTROPIC ELASTICITY The Frithiof Niordson Volume, Proc. DCAMM Int. Symp. on ‘Challenges in Applied Mechanics’, P. Pedersen & N. Olhoff (Eds.), DCAMM, Lyngby (DK), 2003, pp. 263-268.

A procedure for the explicit evaluation of the stationarity points (and hence of

30

absolute maxima and minima) of the strain energy density in anisotropic solids is proposed. The general formulation is provided regardless of the symmetry class to which the solid belongs. Then an illustrative example is given, with application to the case of tetragonal symmetry.

KEY WORDS: strain energy, critical points, anisotropy, tetragonal symmetry.

Paper No. 58 CV1

Papa E., Taliercio A.

CREEP MODELLING OF MASONRY HISTORIC TOWERS in ‘Structural Studies, Repairs and Maintenance of Heritage Architecture VIII’, C.A. Brebbia (Ed.), WIT Press, Southampton (GB), 2003, pp. 131-140.

This work illustrates a theoretical model developed to reproduce the behaviour of ancient masonry subjected to sustained stresses. Starting from a model recently proposed by the authors, two damage tensors have been introduced into a rheological model: the components of these tensors change both according to the intensity of the applied stress and, in case of sustained stress, to the duration of the load history. Evolution laws found in the literature for brittle materials have been employed. The principal directions of damage are meant to represent the directions of the experimental cracks; accordingly, when any damage direction is activated, it remains unchanged throughout the subsequent load history. The presence of second-order damage tensors makes it possible to describe the damage-induced anisotropy of the microcracked material. Also, since the possible increase of damage in time is accounted for, the model is able to describe creep failure and to predict the creep time to failure of the material under given stresses. The model parameters can be obtained through uniaxial creep tests on masonry samples at increasing stress levels and up to failure. The model was implemented into a finite element code, and structural analyses were carried out to assess the safety of middle-age masonry towers. The results obtained for one of these towers are briefly described and discussed.

KEY WORDS: masonry, damage, creep failure, rheological models, sustained loading, finite elements.

Paper No. 59 CV1

Papa E., Taliercio A.

A THEORETICAL MODEL FOR THE DESCRIPTION OF STATIC AND CREEP-INDUCED DAMAGE IN BRITTLE MATERIALS UNDER NON-PROPORTIONAL LOADING in ‘Computational Plasticity VII – Fundamentals and Applications’, D.R.J. Owen, E. Oñate and B. Suàrez (Eds.), CIMNE, Barcelona (E), 2003 (CD ROM).

A theoretical model suitable for the description of the time evolution of

31

mechanical damage in concrete and masonry structures is presented. Starting from a recent proposal of the authors, based on the incorporation of damage variables in the rheological Burger’s model, a numerical model is obtained capable of accounting for creep-induced damage phenomena that affect the mechanical properties of the material. The model is extended to the three-dimensional case, by making use of damage variables of tensorial nature. A peculiar feature of the model is that the principal direction of damage, which are somehow associated to the presence of “cracks” in the material, do not rotate as the stress history evolves in time, leading to a sort of non-rotating smeared-crack model. The capabilities of the model in describing the mechanical response of material elements subjected to non-proportional loading are illustrated. Also, some numerical examples show the possibility to capture the three phases of creep peculiar of brittle materials subjected to heavy persistent stresses, namely primary, secondary and tertiary creep. In the present version, the model is found to be appropriate for rubble-like masonry and concrete, which can be macroscopically assumed to be isotropic in the undamaged state.

KEY WORDS: damage, creep, failure, anisotropy, masonry.

Paper No. 60 CV2

Papa E., Taliercio A.

MODELING OF DAMAGE IN MASONRY UNDER NON PROPORTIONAL LOADING (IN ITALIAN) Atti Workshop su ‘Danneggiamento, conservazione e manutenzione di strutture murarie e lignee: diagnosi e modellazione con riferimento alle tipologie costruttive ed edilizie’, DIS – Politecnico di Milano, January 16-17, 2003, pp. 81-87, L. Binda (Ed.), Eliocenter, Milan.

This work illustrates a model developed to reproduce the behaviour of ancient masonry structures subjected to loads either constant or non-proportionally varying in time. Starting from a model recently proposed by the authors, two damage tensors are introduced whose components evolve both according to the intensity and the duration of the applied stress. Each damage direction is supposed to be associated with the normal to any microcrack that forms and develops at any point of the solid. Accordingly, when a damage direction is activated, it remains fixed whatever the subsequent stress and strain history be. The presence of second order damage tensors allows damage-induced anisotropy to be described and creep failure of the material to be predicted. The model was implemented in a commercial finite element code. The ability of the model to capture the failure mode of a collapsed structure and actual crack patterns is shown by the results of analyses carried out on the Civic Tower of Pavia and the Belltower of Monza Cathedral.

KEY WORDS: damage, creep, failure, anisotropy, masonry.

32

Paper No. 61 CV1

Rovati M., Taliercio A.

ON COAXIALITY OF STRESS AND STRAIN FIELDS AND STATIONARITY OF ELASTIC ENERGY IN ANISOTROPIC SOLIDS Proc. 5th World Congr. on Structural and Multidisciplinary Optimization (WCSMO5), Lido di Jesolo (I), May 19-23, 2003 (CD ROM), 6 pp.

Coaxiality of the stress and strain tensors is a necessary condition for the stationarity of the strain energy density in linearly elastic anisotropic solids. This condition is exploited to explicitly evaluate the critical points of the energy, for a given state of strain, when a material element is rotated respect to the principal directions of strain. The complete solution, in terms of critical points and classification of the corresponding energy values, is given for solids endowed with cubic, hexagonal-5 and tetragonal-6 symmetry. Some preliminary results concerning the more general case of orthorhombic symmetry are also presented.

KEY WORDS: anisotropic elasticity, strain energy density, material symmetries.

Paper No. 62 CV2

Rovati M., Taliercio A.

STRAIN ENERGY EXTREMA FOR ANISOTROPIC SOLIDS (in Italian) Proc. XVI Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Ferrara (I), September 9-12, 2003 (CD ROM), 10 pp.

A general procedure for the explicit evaluation of all the critical points (hence, of absolute maxima and minima) of the strain energy density in anisotropic solids is shown. First, the general formulation is given irrespective of the symmetry class to which the solid belongs. Then, referring to the tetragonal, hexagonal and cubic symmetries, all the stationarity points are explicitly evaluated.

KEY WORDS: strain energy, critical points, Euler’s angles, anisotropy.

Paper No. 63 RV1

Papa E., Taliercio A.

A VISCO-DAMAGE MODEL FOR BRITTLE MATERIALS UNDER NON-PROPORTIONAL MONOTONIC AND SUSTAINED STRESSES Int. J. for Numerical and Analytical Methods in Geomechanics, Vol. 29, No. 3, pp. 287-310, 2005.

A theoretical model is proposed to describe the evolution of damage in brittle materials, such as concrete and masonry, subjected to increasing or sustained stresses of relatively high intensity. The model is based on the introduction of suitable damage variables in a rheological model. In this way, it is possible to

33

describe the material behaviour under stresses either increasing or constant in time. The capabilities of the model in describing the mechanical response of material elements subjected to different stress histories are illustrated. Some correlations with experimental data from tests performed on masonry and concrete specimens are presented, to assess the reliability of the theoretical predictions. The results of some numerical applications to non--proportional stress paths are also illustrated. Finally, the limitations of the proposal are discussed and possible further improvements are envisaged.

KEY WORDS: creep, damage, concrete, anisotropy, numerical algorithms.

Paper No. 64 CV1

Taliercio A.

2D FINITE ELEMENT MODEL FOR THE ANALYSIS OF ELASTIC-PLASTIC COMPOSITES SUBJECTED TO 3D STRESSES Proc. 7th Int. Conf. on Computational Structures Technology, Lisbon, September 7-9, 2004, B.H.V. Topping & C.A. Mota Soares (Eds.), Civil-Comp Press, Stirling, Scotland (UK), paper 51 (CD-ROM), 13 pp.

This work deals with the prediction of the macroscopic response of ductile composites reinforced by a regular array of long, parallel fibers, subjected to any 3D stress, in the plastic range and up to failure. This task is accomplished through a micromechanical approach, based on homogenization theory for periodic media. Special finite elements are formulated to analyze any cross-section of the Representative Volume of the material (a prism of unlimited length, embedding a single fiber) under ‘generalized plane strain conditions’ (i.e., with strain fields invariant along the fiber axis). Particular kinematic conditions are enforced along the boundary of the model to accommodate the periodicity of the microscopic strain field. Such a model turns out to be definitely advantageous in terms of allocated memory and number of kinematic constraints to be enforced, in comparison with fully 3D finite element models. Its effectiveness is assessed in predicting the macroscopic response of MMCs beyond the elasticity limit, until a macroscopic yielding is detected. The numerical results match available theoretical and experimental results with a fair degree of accuracy.

KEY WORDS: finite elements, fiber-reinforced composites, metal-matrix composites.

Paper No. 65 CV2

Taliercio A., Ramalho M.A., Papa E.

A NONLINEAR MODEL FOR MULTI−LEAF MASONRY (in Italian) Proc. of the Workshop ‘Dalla conoscenza e dalla caratterizzazione dei materiali e degli elementi dell’edilizia storica in muratura ai provvedimenti compatibili di consolidamento’, DIS – Politecnico di Milano, December 16-17, 2004, pp. 53-64 (CD-

34

ROM).

A numerical nonlinear model was developed to analyze the mechanical behaviour of multi−leaf masonry, a type of building technique frequently encountered in ancient structures. A damage model, previously developed by some of the authors, was adapted to fit stress−strain curves obtained though tests performed on the single layers of multi−leaf panels, either made of stones with mortar joints, or mortar and aggregate. In this model, damage is characterized by a second−order, symmetric tensor, whose eigenvectors are associated with the crack orientation and remain fixed once any crack is activated, whatever the subsequent load history be. The modified model was implemented into a nonlinear finite element code. Its reliability was assessed through comparisons with results of tests performed on three−leaf masonry panels. Most of the numerical analyses predict the experimentally measured peak load with good accuracy. Usually, the post-peak behaviour is not satisfactorily described: this is likely to be attributed to numerical instabilities, which will be overcome in future developments.

KEY WORDS: masonry, stone, mortar, damage, finite elements, experimental testing.

Paper No. 66 RV1

Taliercio A.

GENERALIZED PLANE STRAIN FINITE ELEMENT MODEL FOR THE ANALYSIS OF ELASTOPLASTIC COMPOSITES Int. J. Solids Structures, Vol. 42, No. 8, pp. 2361-2379, 2005.

A numerical model is presented, based on the finite element method in its displacement formulation, aimed at the analysis of the representative volume element (RVE) of composites reinforced by a regular array of long, parallel fibers, subjected to any 3-D macroscopic stress or strain state. Special finite elements are formulated, which are capable of describing three-dimensional deformation modes associated with strain fields invariant along the fiber axis. Periodicity boundary conditions at the sides of the RVE complete the kinematic formulation. The model is applied to metal-matrix composites, assuming an elastic-perfectly plastic behaviour for both phases; the compatibility matrix of the finite elements is modified, according to proposals of other authors, to avoid locking phenomena near the fully plastic range. Some numerical applications are shown to illustrate the possibility of employing the model to predict the macroscopic response of metal-matrix composites in the non-linear field and up to failure. Comparisons with analytical and experimental results available in the literature testify the reliability of the model estimates.

KEY WORDS: fiber−reinforced composites, metal−matrix composites, plasticity, finite elements, homogenization.

35

Paper No. 67 CV1

Ramalho M.A., Papa E., Taliercio A., Binda L.

A NUMERICAL MODEL FOR MULTI−LEAF STONE MASONRY Proc. XI Int. Conf. on Fracture (ICF-11), Turin (I), March 20-25, 2005, paper #5126 (CD-ROM).

This paper presents a non-linear finite element material model for the analysis of the mechanical behaviour of multi-leaf masonry, which is quite commonly encountered in ancient stone masonry buildings. A damage model, previously developed by some of the authors for brittle materials (namely, concrete) was adapted to fit the experimental stress−strain behaviour of stone masonry. To this end, a damage evolution law originally proposed for concrete was modified and a new material parameter was added. A distinguishing feature of this model is that damage is modelled by a second-order tensor, thus allowing oriented ‘cracks’ to be described; the orientation of the cracks is fixed once they are activated, whatever the subsequent stress history be. Then, the modified model was implemented into a subroutine, linked to a commercial finite element code suitable for nonlinear analyses (FEAP). In order to validate the obtained material model, results available from tests on three-leafed stone masonry prisms were employed. The damage evolution law was calibrated according to results obtained from the single layers, individually tested. The numerical nonlinear structural response was obtained by prescribing suitable displacements boundary conditions and employing a tangent stiffness matrix procedure. In nearly all the applications, the finite element analyses predicted the experimentally measured peak load with good accuracy. However, the post−peak behaviour was not always satisfactorily described: this is likely to be attributed to some numerical instability, which will be overcome in a future version of the model.

KEY WORDS: masonry, stone, mortar, damage, finite elements, experimental testing.

Paper No. 68 CV1

Ramalho M.A., Taliercio A., Anzani A., Binda L., Papa E.

EXPERIMENTAL AND NUMERICAL STUDY OF MULTI-LEAF MASONRY WALLS in ‘Structural Studies, Repairs and Maintenance of Heritage Architecture IX’, C.A. Brebbia & A. Torpiano (Eds.), WIT Press, Southampton (GB), 2005, pp. 333-342.

A research programme was carried out with the aim of investigating the mechanical behaviour of multiple-leaf stone masonry walls. A number of experimental tests were performed on three-leaf specimens, consisting of two external leaves made of stone bricks and mortar joints, and an internal leaf in mortar and stone aggregate. The specimens differed from each other in terms of interface geometry, stone nature, and loading conditions. A numerical model was developed to predict the nonlinear response of the specimens. The model is

36

characterized by a damage tensor, which allows one to describe the damage-induced anisotropy accompanying the cracking process. Comparisons between the predicted and measured failure loads are quite satisfactory in most of the studied cases. The numerical procedure still needs to be improved to accurately describe the post-peak behaviour, by avoiding mesh-dependency effects related to the strain-softening behaviour of the material.

KEY WORDS: masonry, stone, mortar, damage, finite elements.

Paper No. 69 CV1

Anzani A., Binda L., Taliercio A.

EXPERIMENTAL AND NUMERICAL STUDY OF THE LONG TERM BEHAVIOUR OF ANCIENT MASONRY in ‘Structural Studies, Repairs and Maintenance of Heritage Architecture IX’, C.A. Brebbia & A. Torpiano (Eds.), WIT Press, Southampton (GB), 2005, pp. 577-586.

A study on the time dependent behaviour of the masonry coming from the XVI century crypt of the Cathedral of Monza (Italy) will be described. The simulation of the observed behaviour by a visco-elastic rheological model, including damage variables, will be presented for a subsequent application to construction analysis.

KEY WORDS: ancient masonry, creep, viscoelasticity, damage.

Paper No. 70 CV1

Anzani A., Binda L., Taliercio A.

APPLICATION OF A DAMAGE MODEL TO THE STUDY OF THE LONG TERM BEHAVIOUR OF ANCIENT TOWERS Proc. 1st Canadian Conference on ‘Effective Design of Structures’, Hamilton, Ontario (CND), July 10-13, 2005, pp. 401-411.

A further step toward the understanding of the mechanical behaviour of ancient masonry under persistent loading is taken, thanks to a new experimental research performed on the masonry of the collapsed medieval tower of Pavia, subjected to pseudo-creep tests. The laboratory results are interpreted with the help of a visco-elastic rheological model, including damage variables, for a subsequent application to construction analysis.

KEY WORDS: ancient masonry, creep, viscoelasticity, damage.

Paper No. 71 CV1

Papa E., Taliercio A.

37

A NON-ROTATING ANISOTROPIC DAMAGE MODEL FOR BRITTLE MATERIALS in ‘Computational Plasticity VIII – Fundamentals and Applications’, D.R.J. Owen, E. Oñate & B. Suàrez (Eds.), CIMNE, Barcelona (E), Part 2, pp. 857-860, 2005.

A theoretical model is presented suitable for the description of the damaging process in brittle materials. Damage is defined by a second-order symmetric tensor and activates at different orientations to the principal strain directions, according to the sign of the principal strain which attains a damage threshold. The capabilities of the model in describing the mechanical response of material elements subjected to non-proportional stresses are illustrated.

KEY WORDS: damage, anisotropy, microcrack, masonry, concrete.

Paper No. 72 CV2

Rovati M., Taliercio A., Veber D.

TOPOLOGICAL OPTIMIZATION FOR MICROPOLAR SOLIDS (in Italian) Proc. XVII Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Florence (I), September 11-15, 2005, 12 pp. (CD-ROM).

The theory of micropolar continua is an extension of the classical theory of Cauchy’s continua. In this paper a procedure is proposed for the topological optimization of structures made of micropolar solids in view of the maximization of their elastic stiffness. The minimum flexibility problem, with a constraint on the volume fraction, is solved through an augmented Lagrangian functional. Some numerical examples are shown, focusing in particular on structural interfaces. The results show that the obtained optimal topologies agree with the real shape of biological tissues and indicate that the proposed procedure can be employed in the definition of the optimal topology of structures made of nonlocal artificial materials.

KEY WORDS: topological optimization, micropolar continua, Cosserat’s theory.

Paper No. 73 CV2

Papa E., Taliercio A., Zavelani Rossi A.

NONLINEAR ANALYSIS OF MASONRY PANELS USING EQUILIBRATED FINITE ELEMENTS (in Italian) Proc. XVII Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Florence (I), September 11-15, 2005, 11 pp. (CD ROM).

In the analysis of masonry walls the accurate definition of the stress components at the brick-mortar interface is of particular importance. In these regions it is more important to have a rigorously equilibrated definition of the stress state rather than a rigorously compatible description of the strain state: this result can

38

be obtained by directly modelling the stress fields and making use of the principle of the minimal complementary energy. An equilibrium approach was previously developed by Zavelani Rossi (2001) based on the definition of linear stress subfields in quadrangular finite elements. The state of stress over each triangular sub-element is rigorously kept under control through a check at the element corners, so that possible critical situations at the inner boundaries can be evidenced. Fractures along the boundary of the elements are identified according to the values of the shear and normal stress components along the contact surface. Using this model three different typologies of masonry structures have been analyzed: a dry stone masonry panel subjected to constant vertical load and progressively increasing horizontal load (Oliveira, 2002); a dry brick masonry panel with an asymmetric rectangular opening subjected to the same load conditions as the previous one (Vermeltfoort el al., 1993); some stone masonry prisms with three leaves subjected to compression or “shear” loads (Pina-Henriques et al., 2004). The numerically predicted crack pattern is generally in good agreement with the experimental findings; the estimated load carrying capacity is comparable to that supplied by compatible finite element models.

KEY WORDS: masonry, equilibrated finite elements, friction, cohesion.

Paper No. 74 RV1

Anzani A., Binda L., Ramalho M.A., Taliercio A.

HISTORICAL MULTI-LEAF MASONRY WALLS: EXPERIMENTAL AND NUMERICAL RESEARCH Masonry International, Vol. 18, No. 3, pp. 101-114, 2005.

Following several failures of historic buildings occurred in the recent past, a research programme was carried out with the aim of investigating the mechanical behaviour of multiple-leaf stone masonry walls. A number of experimental tests were performed on three-layered specimens, consisting of two external leaves made of regularly cut stones and mortar joints, and an internal leaf simulating a rubble filling. The tests differed in terms of interface geometry and stone nature of the specimens, and in terms of loading conditions. A numerical model was developed to predict the nonlinear response of the specimens. The model is characterized by a damage tensor, which allows for the description of the damage-induced anisotropy accompanying the cracking process. Comparisons between the predicted and measured failure loads and average stiffness of the specimens are quite satisfactory in most of the studied cases. The numerical procedure still needs to be improved to accurately describe the post-peak behaviour, by avoiding mesh-dependency effects related with the strain-softening behaviour of the material.

KEY WORDS: masonry, multi-leaf walls, stone, mortar, damage, testing, finite elements.

39

Paper No. 75 CV1

Taliercio A., Binda L.

STRUCTURAL ANALYSIS OF THE BYZANTINE BASILICA OF SAN VITALE IN RAVENNA Proc. Int. Conf. ‘Structural Faults and Repair-2006’, Edinburgh, Scotland (UK), June 13-15, 2006, 12 pp. (CD ROM).

A finite element model was developed to analyse the Byzantine Basilica of San Vitale in Ravenna (Italy); modelling is intended to help understanding the origin of a diffused crack pattern in the building. In the structural analyses account was taken of the permanent loads and the seasonal thermal changes. Because of the complexity of the geometric model, a simplified (linearly elastic, isotropic) constitutive law had to be assumed to keep the computing time within reasonable limits. Accordingly, the performed analyses constitute only a first step toward the understanding of the structural behaviour of the Basilica, as the adopted constitutive law cannot fully explain the surveyed crack pattern, which is influenced by the brittleness and the anisotropy of the constituent materials. It is shown, however, that the self-weight alone is largely responsible for the current state of damage in the Basilica. The numerically predicted seasonal change in displacements match the measurements of a monitoring network taken every six months, which proves the reliability of the finite element model.

KEY WORDS: masonry, Byzantine basilica, survey, settlements, cracking.

Paper No. 76 CV1

Taliercio A.

PREDICTING THE MACROSCOPIC BEHAVIOUR OF METAL-MATRIX COMPOSITES EMBEDDING AN INTERPHASE Proc. 8th Int. Conf. on Computational Structures Technology, Las Palmas de Gran Canaria (E), September 12-15, 2006, B.H.V. Topping, G. Montero & R. Montenegro (Eds.), Civil-Comp Press, Stirlingshire, Scotland (UK), paper 269 (CD-ROM), 15 pp. (doi:10.4203/ccp.83.269).

A numerical model previously developed by Taliercio is applied to the prediction of the macroscopic nonlinear behaviour of unidirectional metal-matrix composites (MMCs), considering the presence of an interphase region between the fibres and the matrix. Special 2D finite elements are formulated, capable of describing Generalized Plane Strain conditions for a representative unit cell of the composite, that is, 3D deformation modes invariant along the fibre axis. Periodicity conditions at the boundary of the cell complete the kinematic formulation. The three phases of the composite are supposed to be elastic-perfectly plastic and to conform with J2-plasticity. Some numerical applications are carried out to investigate the influence of the interphase material on the macroscopic strength of the composite under elementary stress states.

40

KEY WORDS: fiber reinforced composites, metal-matrix, interphase, homogenization, finite elements.

Paper No. 77 CV1

Taliercio A., Binda L.

STRESS ANALYSIS OF THE BYZANTINE BASILICA OF SAN VITALE IN RAVENNA: EVALUATION OF ITS CURRENT STATE AND MID-TERM PREDICTIONS in ‘Structural analysis of historical constructions’, P.B. Lourenço, P. Roca, C. Modena, S. Agrawal (Eds.), McMillan India Ltd, New Delhi (India), pp. 2005-2012, 2007.

A finite element model was developed to analyze the Basilica of San Vitale in Ravenna, a Byzantine building which suffers diffused cracking and excessive deformation. In the structural analyses account was taken of permanent loads and ground settlements increasing in time. The tensile stresses predicted by a linear elastic stress analysis agree with most of the observed cracks. Assuming the ground settlements to increase at the currently estimated rate, the stresses in several parts of the Basilica might seriously endanger the stability of the building during the present century.

KEY WORDS: masonry, Byzantine basilica, survey, settlements, cracking.

Paper No. 78 RV2

Taliercio A., Binda L.

ON THE RELIABILITY OF LINEAR ELASTIC ANALYSES OF HISTORICAL MASONRY BUILDINGS: A CASE STUDY J. Build. Apprais., Vol. 2, No. 4, pp. 301-312, 2007.

A finite element model was developed to analyse the Byzantine Basilica of San Vitale in Ravenna (Italy); modelling is intended to help understanding the origin of a diffused crack pattern in the building. In the structural analyses, account was taken of the permanent loads and the seasonal thermal changes. Owing to the complexity of the geometric model, a simplified (linearly elastic, isotropic) constitutive law had to be assumed to keep the computing time within reasonable limits. Accordingly, the adopted constitutive law cannot fully explain the surveyed crack pattern, which is influenced by the brittleness and the anisotropy of the constituent materials; thus, the performed analyses constitute only a first step towards the understanding of the structural behaviour of the Basilica. It is shown, however, that the self-weight alone is largely responsible for the current state of damage in the Basilica. The numerically predicted seasonal change in displacements agree fairly well with the measurements of a monitoring network taken every six months, which proves the reliability of the finite element model.

41

KEY WORDS: masonry, Byzantine Basilica, finite elements, survey, settlements, cracking.

Paper No. 79 RV1

Taliercio A., Binda L.

THE BASILICA OF SAN VITALE IN RAVENNA: INVESTIGATION ON THE CURRENT STRUCTURAL FAULTS AND THEIR MID-TERM EVOLUTION Journal of Cultural Heritage, Vol. 8, No. 2, pp. 99-118, 2007.

A finite element model was developed to analyze the Basilica of San Vitale in Ravenna (Italy), a Byzantine building which suffers diffused cracking and excessive deformation, mainly as a consequence of complex architectural vicissitudes (extensions, demolitions …) and ground settlements. In the structural analyses, account was taken of permanent loads (self-weight), boundary displacements increasing in time, and seasonal thermal changes. Thanks to previous topographical surveys of part of the building, to chemical and mechanical investigations, the geometry of the Basilica and the main physical properties of the materials are reasonably well defined. The geometric model does not virtually neglect any structural element and accounts for the lack of symmetries in the building. Because of the complexity of the geometric model, a simplified (linearly elastic, isotropic) constitutive law had to be assumed to keep the computing time within reasonable limits. Accordingly, the performed analyses constitute only a first step toward the understanding of the structural behaviour of the Basilica, as the adopted constitutive law can only partially explain the surveyed crack pattern, which is influenced by the brittleness and the anisotropy of the constituent materials.

Key words: Byzantine Basilica, masonry, ground settlements, thermal changes, cracking, monitoring, finite elements.

Paper No. 80 CV1

Ramalho M.A., Papa E., Taliercio A.

A NON−LOCAL ANISOTROPIC DAMAGE MODEL FOR BRITTLE MATERIALS in ‘Structural Studies, Repairs and Maintenance of Heritage Architecture X’, C.A. Brebbia (Ed.), WIT Press, Southampton (GB), 2007, pp. 505-514.

A non-local damage model is proposed for brittle materials, such as masonry and concrete, starting from a previous proposal of the authors. The model is characterized by a symmetric, second order damage tensors, which accounts for strain-induced anisotropy. Different laws are employed to describe the evolution of damage induced by tensile or compressive strains. The principal directions of damage remain fixed throughout any load history, and a non-rotating smeared crack model is obtained. The model overcomes some deficiencies of the previous local version, as damage at any point is computed according to the strain

42

averaged over a suitable neighbourhood of that point, thus alleviating mesh-dependency effects. The model is successfully applied to the analysis of three-leaf walls tested to failure under different load conditions.

KEY WORDS: masonry, concrete, non-local damage, anisotropy, mesh sensitivity.

Paper No. 81 CV1

Taliercio A.

MACROSCOPIC STRENGTH ESTIMATES FOR DUCTILE THREE-PHASE FIBER-REINFORCED COMPOSITES in ‘Computational Plasticity IX − Fundamentals and Applications’, E. Oñate, D.R.J. Owen & B. Suàrez (Eds.), CIMNE, Barcelona (E), Part 1, pp. 429-432, 2007.

The influence of a weakening interphase region on the macroscopic strength of metal-matrix composites (MMCs) is investigated. Assuming the three phases of the composite to be elastic-perfectly plastic, theoretical bounds to its macroscopic strength domain are derived by applying the fundamental theorems of limit analysis within the framework of homogenization theory for periodic media. Analytical expressions are obtained for the bounds to the macroscopic strength under special uni- and two-dimensional stress conditions.

KEY WORDS: metal-matrix composites, interphase, homogenization, limit analysis.

Paper No. 82 CV1

Gentile C., Taliercio A.

THE PHENOMENON OF VEERING IN THE ASSESSMENT OF R.C. ARCH BRIDGES Proc. 5th Int. Conf. on Arch Bridges (ARCH’07), Funchal, Madeira (P), September 12-14, 2007, P.B. Lourenço, D.V. Oliveira & A. Portela (Eds.), pp. 425-431.

In this paper, possible sources of eigenvalue curve veering in arch bridges are sought. First, curve veering for an existing r.c. arch bridge is shown to be the effect of either a change in the elastic modulus of concrete, or the presence of zones with different stiffness. Then, the theoretical analysis of this phenomenon is carried out for an arch where a small region exists with elastic properties different from the remaining structure. The former example is meant to show that real arch bridges can be prone to the eigenvalue curve veering; hence, the experimental observation of veering should effectively address the identification of the structural parameters. In addition, the latter example suggests that, in some instances, localized damage in an existing bridge can be identified through the occurrence of eigenvalue curve veering.

KEY WORDS: arch bridges, assessment, veering, eigenfrequencies, eigenmodes, damage.

43

Paper No. 83 CV2

Veber D., Taliercio A.

EXTREMA OF THE STRAIN ENERGY DENSITY FOR ANISOTROPIC MICROPOLAR SOLIDS Proc. XVIII Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Brescia (I), September 11-14, 2007, 12 pp. (CD ROM).

The paper deals with any 2D solid of prescribed shape and elastic properties, consisting of an orthotropic micropolar material. The conditions are determined under which the global stiffness of the solid is maximized, taking the orientation θ of the material symmetry axes to the local extreme strains as design variable. Unlike Cauchy solids, it is shown that the maximum stiffness problem for micropolar solids is not fulfilled by ‘trivial’ solutions, at which full collinearity of the material symmetry axes and the directions of the extreme strains is achieved. The paper closes with the determination of the optimal orientations for a special elasticity problem.

KEY WORDS: micropolar solid, anisotropy, strain energy density, optimization.

Paper No. 84 RV1

Taliercio A.

MACROSCOPIC STRENGTH ESTIMATES FOR METAL MATRIX COMPOSITES EMBEDDING A DUCTILE INTERPHASE Int. J. Solids Structures, Vol. 44, No. 22-23, pp. 7213-7238, 2007.

The influence of an interphase region on the macroscopic strength of unidirectional fiber-reinforced metal-matrix composites (MMCs) is investigated. The three phases of the composite are supposed to be elastic-perfectly plastic and to conform with J2-plasticity. First, theoretical bounds to the macroscopic strength are derived, according to homogenization theory for heterogeneous periodic media: the gap between these bounds is quite narrow for certain stress conditions, volumetric proportions of the constituents, and ratios of the interphase-to-matrix strength. Then, a numerical model previously developed by Taliercio (2005) is employed to predict the macroscopic response of three-phase MMCs under any 3D stress through the analysis of a single representative unit cell. The model is applied to the numerical identification of the macroscopic strength properties of MMCs under uni-, bi- and triaxial stresses, in cases where the theoretical bounds are not sufficiently close to identify the actual macroscopic yield surface. The influence of the weakening interphase on the predicted macroscopic strength is critically discussed. A decrease in interphase strength is found to affect the transverse tensile and shear strength of the composite to a moderate extent, whereas the macroscopic longitudinal shear strength is extremely sensitive to the interphase strength.

44

KEY WORDS: fiber-reinforced composites, metal-matrix, interphase, homogenization, finite elements.

Paper No. 85 CL1

Taliercio A., Papa E.

MODELLING OF THE LONG-TERM BEHAVIOUR OF HISTORICAL MASONRY TOWERS in: ‘Learning from Failure: Long-term Behaviour of Heavy Masonry Structures’, L. Binda (Ed.), WIT Press, Southampton (GB), 2007, Chapter 7, pp. 153-173.

In March 1989 the Civic Tower in Pavia suddenly collapsed, killing four people and destroying part of the adjacent Cathedral, along with some of the buildings overlooking the surrounding square. No special event, to which the collapse might be attributed, was monitored in the preceding months. Also, no evidence of significant soil settlements was found. The results of a number of accelerated creep tests performed on samples extracted from the debris, along with finite element (FE) analyses of the tower, indicated that a possible origin for the collapse was the cumulation of creep-induced damage in time. Indeed, under sustained loading some of the specimens failed at stress levels comparable to the maximum values yielded by the numerical analyses. This remark was the starting point for an extensive research programme aiming at (1) characterizing the creep behaviour of ancient masonry; (2) developing theoretical models suitable to the description of creep evolution and creep-induced damage; and, finally, (3) assessing the safety of ancient masonry buildings subjected to heavy persistent loads through nonlinear structural analyses. In this chapter, a theoretical model developed by the authors is first described; the procedure employed to identify the model parameters from results of accelerated creep tests is also outlined. Then, the numerical results of structural analyses of two masonry towers are presented, with particular emphasis on the description of the damage evolution in time, up to the predicted creep time to failure for the building. Finally, the obtained results are critically reviewed, and future improvements for the theoretical model are pointed out.

KEY WORDS: historical masonry, towers, creep, damage.

Paper No. 86 RV1

Ramalho M.A., Taliercio A., Anzani A., Binda L., Papa E.

A NUMERICAL MODEL FOR THE DESCRIPTION OF THE NONLINEAR BEHAVIOUR OF MULTI-LEAF MASONRY WALLS Adv. Eng. Soft., Vol. 39, No. 4, pp. 249-257, 2008.

A nonlinear finite element model was developed to simulate the nonlinear response of three-leaf masonry specimens, which were subjected to laboratory tests with the aim of investigating the mechanical behaviour of multiple-leaf

45

stone masonry walls up to failure. The specimens consisted of two external leaves made of stone bricks and mortar joints, and an internal leaf in mortar and stone aggregate. Different loading conditions, typologies of the collar joints, and stone types were taken into account. The constitutive law implemented in the model is characterized by a damage tensor, which allows the damage-induced anisotropy accompanying the cracking process to be described. To follow the post-peak behaviour of the specimens with sufficient accuracy it was necessary to make the damage model nonlocal, to avoid mesh-dependency effects related to the strain-softening behaviour of the material. Comparisons between the predicted and measured failure loads are quite satisfactory in most of the studied cases.

KEY WORDS: multi-leaf masonry, testing, damage, anisotropy, finite elements, non-local damage, mesh-sensitivity.

Paper No. 87 CV1

Freitas A.A., Ramalho M.A., Corrêa M.R.S., Taliercio A.

NUMERICAL AND EXPERIMENTAL ANALYSIS OF CONCRETE BLOCK PRISMS UNDER COMPRESSION Proc. 14th International Brick/Block Masonry Conference (IB2MAC), Sydney, February 17-20, 2008, paper #165, 10 pp. (CD ROM).

This paper presents a comparison between experimental and numerical analysis of concrete block prisms under compression loads. The main goal of the study is to simulate the behavior of prisms based on the behavior of blocks and mortar joints using a numerical non-local damage model specially developed for quasi-brittle materials. An experimental program, with displacement control, is carried out to determine damage parameters and the complete load-displacement diagram of the prisms. Numerical models are then used to evaluate the behavior of the prisms. Obtained results show that the considered non-local damage model is able to predict the failure and the softening regime of the prisms.

KEY WORDS: concrete blocks, mortar, testing, finite elements, non-local damage.

Paper No. 88 CV1

Ramalho M.A., Taliercio A.

NON-LOCAL DAMAGE PROCEDURE BASED ON WEIGHTED AVERAGING OF THE STRAIN FIELD (in Portuguese) XXXIII Jornadas Sudamericanas de Engenieria Estructural, Santiago del Chile, May 26-30, 2008, 10 pp. (CD ROM).

This paper deals with the behavior of brittle materials by way of an efficient non-local damage procedure. It is performed a weighted average of the strain field over a suitable neighborhood for assessing the strain field at a point avoiding

46

mesh dependency. Initially, a summary about the non-local procedures and its implementation on a general finite element program and FEAP program is discussed. Two different ways to select the neighbor elements and three weight functions are presented. After, the equations for evaluating the strain average at a Gauss point considering the strain field over the neighborhood are shown. Finally, an example of a specimen under compression considering local damage and several non-local damage procedures is presented and discussed, even with the obtained processing time. The conclusions show the best alternatives to be adopted and make clear the utility of the procedure to evaluate the behavior of brittle material structures.

KEY WORDS: Finite Element Method, non-local damage, mesh dependency.

Paper No. 89 CV1

Condoleo P., Taliercio A., Binda L.

SAFETY ASSESSMENT OF TEMPLE E7 IN MỸ SƠN, VIET NAM in ‘Structural analysis of historic construction-Preservation of safety and significance’, D. D’Ayala & E. Fodde (Eds.), Taylor & Francis Group, London, Vol. 1, pp. 635-642, 2008.

The present work illustrates the results of structural analyses carried out on one of the temples located in the archaeological area of Mỹ Sơn in Central Viet Nam. The temple is a relatively well-preserved building, hosting two square chambers covered by false vaults. A corner of the temple was destroyed by a bomb, and some passing-through cracks were likely induced by the vegetation. The temple was built using multi-leaf brick masonry in most of the walls, the outer leaves being more regular in texture than the inner one; also, the bricks in the outer leaves are stuck by natural resin, which provides an excellent bonding. Finite element models of the temple were set up, according to an accurate recently performed survey, and to drawings dating back to the beginning of the 20th century, as far as the geometry of the nearly intact building is concerned. The models take the layered nature of masonry into account. The masonry leaves were supposed to be either perfectly or partially connected, allowing for a Mohr-Coulomb’s type failure condition at the interface between adjacent leaves. Numerical analyses were carried out to evaluate the presumable stress conditions of the still intact temple and to determine whether or not the self-weight alone might be the cause for the collapse of parts of the temple. Also, the damages induced by bombs and vegetation were taken into account, and the current stress conditions were determined. Some conclusions on the safety of the temple in its past and current conditions are drawn; also, the influence of the models employed to allow for the contact between the different masonry layers is discussed.

KEY WORDS: Champa temple, multiple leaf masonry, finite elements, debonding.

47

Paper No. 90 CV1

Condoleo P., Taliercio A., Binda L.

PAST AND CURRENT STRESS CONDITIONS OF TEMPLE G1 IN MỸ SO’N, VIETNAM Proc. Int. RILEM Conf. on Site Assessment of Concrete, Masonry and Timber Structures (SACoMaTiS 2008), Varenna (I), September 1-2, 2008, L. Binda, M. di Prisco & R. Felicetti (Eds.), Vol. 2, pp. 913-922.

The work describes a survey of one of the Hindu temples of the monumental area of My Son in central Vietnam, named G1 by Parmentier at the beginning of the XX century. Also, the paper illustrates the results of numerical analyses of the temple both at its current state and at its presumed original conditions. The temple is in a rather bad state, as most of the vaults were already collapsed at the time of Parmentier’s expedition, and further on destroyed during the Vietnam War. Numerical analyses were carried out to evaluate the presumable stress conditions of the still intact temple and determine whether or not the self-weight alone might be the cause for the partial collapse. Also, the current stress conditions were determined, to avert any further possibility of failure. The numerical models take the layered nature of masonry into account. The masonry leaves were supposed to be either perfectly connected or independent, the last one being the less conservative assumption.

KEY WORDS: multi leaf masonry, Champa temple, finite elements, interface.

Paper No. 91 CV1

Boothby Th.E., Condoleo P., Taliercio A., Binda L.

DEVELOPING MASONRY VAULT MODELS FOR GLOBAL ASSESSMENT Proc. Int. RILEM Conf. on Site Assessment of Concrete, Masonry and Timber Structures (SACoMaTiS 2008), Varenna (I), September 1-2, 2008, L. Binda, M. di Prisco & R. Felicetti (Eds.), Vol. 2, pp. 551-560.

The development of a model for a masonry vault involves a complex series of interrelated decisions on geometry, modeling, material selection, meshing, and boundary conditions. It is necessary from the outset to decide the level of simplification that will be applied to the actual geometry of the structure. This decision takes account of the information desired from the model, the quantity and accuracy of the geometric information available. The use of shell or solid elements dictates both the constraints on meshing the model and the subsequent performance of the model. The boundary conditions are both critical to the results of the model and extremely difficult to assess. In this article, we present the process of working from a large amount of survey information to develop first a viable geometrical model, then the process of meshing used to make this into a working finite element model, and finally the process of using field-acquired vibration data to update the model as necessary.

48

KEY WORDS: masonry, gothic church, domical cross vault, geometrical survey, finite elements.

Paper No. 92 CV1

Taliercio A., Veber D., Mola A.

NUMERICAL SOLUTIONS FOR SOME AXISYMMETRIC ELASTIC MICROPOLAR ORTHOTROPIC BODIES Proc. 9th Int. Conf. on Computational Structures Technology, Athens, September 2-5, 2008, B.H.V. Topping & M. Papadrakakis (Eds.), Civil-Comp Press, Stirlingshire, Scotland (UK), paper #253 (CD-ROM), 16 pp.

Some special linear elastic problems for axisymmetric orthotropic micropolar solids with central symmetry are dealt with. The first one is a hollow circular cylinder of unlimited length, subjected to internal and external uniform pressure. The second one is a hollow or solid circular cylinder of finite length, subjected to twisting moments acting on its bases. In both cases, one of the axes of elastic symmetry is parallel to the cylinder axis; the other two are arbitrarily oriented in the plane of any cross-section of the solid. The elastic properties are invariant along the cylinder axis. The two problems are governed by formally similar sets of ordinary differential equations in the kinematic fields (in-plane displacements and microrotations). In the general case, numerical solutions are derived and critically discussed. Special emphasis is put on the comparison between ‘classical’ Cauchy solution and micropolar solution.

KEY WORDS: micropolar solid, anisotropy, linear elasticity, cylinder, pressure, torsion.

Paper No. 93 RV2

Binda L., Condoleo P., Taliercio A.

RESTORATION OF HINDU TEMPLES IN MỸ SO'N, VIET NAM: EXPERIMENTAL INVESTIGATION, MODELLING AND PROPOSAL FOR INTERVENTION J. Struct. Eng., SERC, Vol. 35, No. 6, pp. 437-442, 2009.

The archaeological site of Mỹ Sơn is located in central Vietnam and is characterized by the presence of several Hindu temples, many of which were heavily damaged during the Viet Nam war in the 1960s. The present work illustrates the results of experimental tests carried out on material samples taken from the temples, and describes the fundamental lines of the preservation project to be undertaken. Finite element models of some of the temples were set up, both at their presumable original state and at their current damaged conditions. The stress analyses of the original temples aimed to establish whether or not the self-weight alone might be the cause for the collapse of parts of the temples. Also, the damages induced by the bombs and the vegetation were taken into account, and

49

the current stress conditions were determined. The FE models take the layered nature of masonry into account; different types of interactions between the masonry leaves were assumed in the analyses. Some conclusions on the safety of the temples in its past and current conditions are drawn; also, the influence of the models employed to describe the interaction between the different masonry layers is discussed..

KEY WORDS: Champa temple, multi-leaf masonry, testing, preservation project, finite elements.

Paper No. 94 CV1

Taliercio A.

AN OVERVIEW ON MASONRY CREEP in ‘Structural Studies, Repairs and Maintenance of Heritage Architecture XI’, C.A. Brebbia (Ed.), WIT Press, Southampton (GB), 2009, pp. 197-208.

This paper intends to give a state of the art on the experimental and theoretical studies regarding masonry creep, considering several papers published on this subject in the last two decades. Both new and historic masonry are addressed. Linear viscoelastic behaviour can be assumed in the analysis of masonry under service loads, whereas damage effects must be taken into account when analyzing the effects of heavy sustained loads, as in the case of several historic buildings. Finally, some applications are shown of a model to the prediction of the time evolution of creep-induced damage in historic masonry towers.

KEY WORDS: masonry, creep, damage.

Paper No. 95 RV1

Taliercio A., Veber D.

SOME PROBLEMS OF LINEAR ELASTICITY FOR CYLINDERS IN MICROPOLAR ORTHOTROPIC MATERIAL Int. J. Solids Structures, Vol. 46, No. 22-23, pp. 3948-3963, 2009.

Some special problems for axisymmetric solids made of linearly elastic orthotropic micropolar material with central symmetry are dealt with. The first one is a hollow circular cylinder of unlimited length, subjected to internal and external uniform pressure. The second one is a hollow or solid circular cylinder of finite length, subjected to a relative rotation of the bases about its axis. In both cases, one of the axes of elastic symmetry is parallel to the cylinder axis; the other two are arbitrarily oriented in the plane of any cross-section of the solid. The elastic properties are invariant along the cylinder axis. It is shown that the two problems are governed by formally similar sets of ordinary differential equations in the kinematic fields (in-plane displacements and microrotations). In the general case, numerical solutions are derived. The solution for the cylinder

50

subjected to radial pressure does not significantly differ from that obtained in classical elasticity, at least in terms of radial and hoop force stresses. In the case of a cylinder subjected to torsion the difference between the micropolar and the classical solutions is more pronounced. The torque induces twisting couple stresses about the cylinder axis of variable sign. Finally, size effects in terms of torsional inertia are pointed out.

KEY WORDS: micropolar solid, anisotropy, linear elasticity, cylinder, pressure, torsion.

Paper No. 96 CV2

Binda L., Taranto P., Condoleo P., Taliercio A.

ANALYSIS OF MASONRY TOWERS EXPERIENCING CLADDING DETACHMENT (in Italian) Proc. Workshop on “Design for rehabilitation of masonry structures” (WONDERmasonry 2009), P. Spinelli & A. De Luca (Eds.), Lacco Ameno (I), October 8−10, 2009, pp. 700-709.

An accurate diagnostic investigation was carried out by the Authors on the Isso Tower in the city of Castelleone. The tower, around 50m high, was built between the 11th and the 12th and underwent heavy interventions toward the middle of the past century, when a reinforced concrete tank for the city water supply was built internally. The load-bearing walls are built in solid bricks, but, according to a technique used in the medieval times, they were covered on the internal and external faces by a cladding one brick thick, which had the function of hiding the rough internal masonry. The most serious source of problems concerning the safety of the structure is represented by the detachment of large portions of this cladding. Part of the investigation had precisely the aim of quantifying, through maps of the detachments, the entity of the damages and of calculating, by a FE model, the effects of the detachments in terms of stresses. This preliminary study is the base for the necessary conservation works that the municipality intends to carry out in order to open the tower to the tourists.

KEY WORDS: middle-age tower, multi-leaf masonry, detachment, diatons, finite elements.

Paper No. 97 CV1

Anzani A., Condoleo P., Gobbo A., Taliercio A.

MODELING THE STATIC BEHAVIOUR OF A DOUBLE CURVATURE BRICKWORK VAULT in ‘Structural analysis of historic constructions-Strengthening and Retrofitting’, X. Gu & X. Song (Eds.), Trans Tech Pub., Zurich (CH), Vol. 1, pp. 367-372, 2010.

For safety assessment, a double curvature hollow bricks cloister vault with

51

lunettes has been studied. Its geometry, constructive aspects, crack pattern have been surveyed and a 3D finite element analysis has been carried out, the numerical model exploiting the accurate survey of the vault geometry.

KEY WORDS: cloister vault, hollow bricks, steel, geometrical survey, numerical modeling.

Paper No. 98 CV1

Veber D., Taliercio A.

TOPOLOGY OPTIMIZATION FOR CHIRAL ELASTIC BODIES Proc. 10th Int. Conf. on Computational Structures Technology, Valencia (E), September 15-17, 2010, B.H.V. Topping, J.M. Adam, F.J. Pallarés, R. Bru & M.L. Romero (Eds.), Civil-Comp Press, Stirlingshire, Scotland (UK), paper #316 (CD-ROM), 11 pp.

The topology optimization problem for linearly elastic micropolar solids is applied to the optimal design of 3D solids made of isotropic micropolar materials. The constituent materials are supposed to generally lack centrosymmetry, which means that force stresses and microcurvatures are coupled, and so are couple stresses and micropolar strains. Non-centrosymmetric materials are also called chiral materials. Chirality is the lack of planes of symmetry in material elements, so that the mirror image of the element is not identical to the element itself. Macroscopically, this is the case of composites with helical or screw-shaped inclusions; particular honeycombs can also be modeled as chiral materials at the macroscale. The maximum global stiffness is taken as the objective function, and the material density as the design variable. According to the solid isotropic material with penalisation (SIMP) model, the constitutive tensors are assumed to be smooth functions of the density. Optimal material distributions are obtained for several significant cases, including beams subjected to axial force and bending. The differences with respect to the optimal configurations obtained with classical Cauchy materials and centrosymmetric materials are pointed out and discussed. Similar to micropolar centrosymmetric solids, the optimum material localizes into curved beam-shaped regions, in contrast to the well-known truss-like solutions that arise in the optimal topological design of Cauchy solids. The inherent material non-symmetry is matched by non symmetric optimal geometries, as the material, in the optimal configuration, must resist the bending and torsional deformation of the structure.

KEY WORDS: topology optimization, micropolar materials, chirality.

Paper No. 99 RV1

Taliercio A.

TORSION OF MICROPOLAR HOLLOW CIRCULAR CYLINDERS Mechanics Research Communications, Vol. 37, No. 4, pp. 406-411, 2010.

52

A hollow cylinder made of a linearly elastic isotropic micropolar material subjected to twist is analyzed. The complete analytical solution is obtained, including the case of a solid cylinder previously dealt with by other authors. The influence of the different material constants on the stress distribution and the torsional rigidity is illustrated. Also, the differences are pointed out between the obtained solution and that for a solid cylinder.

KEY WORDS: torsion, Cosserat elasticity, hollow cylinder.

Paper No. 100 CV1

Taliercio A.

NUMERICAL MODELS TO PREDICT THE CREEP BEHAVIOUR OF BRICKWORK in ‘Structural Studies, Repairs and Maintenance of Heritage Architecture XII’, C.A. Brebbia & L. Binda (Eds.), WIT Press, Southampton (GB), 2011, pp. 671-682, and in ‘Heritage Masonry: Materials and Structures’, S. Syngellakis (Ed.), WIT Press, Southampton (GB), 2013, pp. 169-180.

The numerical modelling of the time evolution of stresses and strains in brickwork under sustained loads is dealt with, within the framework of linear viscoelasticity. Finite element analyses were carried out, using three different masonry models: a simplified 2D layered model, and two 3D models (one for header bond masonry; one for Flemish bond masonry). The creep behaviour of the component materials (bricks and mortar) was defined according to experimental data available in the literature. These results were best fitted by Prony series, and the obtained creep laws were employed to carry out FE analyses of the masonry walls with different textures. Owing to the different mechanical response of the components to sustained loads, the stress and strain distribution in the wall changes in time and differs from that at the beginning of the loading process. The different behaviour of the two considered brick patterns is pointed out. The possibility of applying the simplified layered model instead of refined 3D models to predict the time evolution of stresses and strains is discussed.

KEY WORDS: masonry, creep, linear viscoelasticity, header bond, Flemish bond.

Paper No. 101 CV2

Bruggi M., Taliercio A.

TOPOLOGY OPTIMIZATION OF MICRO-POLAR SOLIDS UNDER DYNAMIC ACTIONS Proc. XX Congress of the Italian Association of Theoretical and Applied Mechanics (AIMETA), Bologna (I), September 12-15, 2011, 10 pp. (CD ROM).

The topology optimization problem for micropolar solids subjected to dynamic

53

loads is dealt with. Goal of the problem is the maximization of the minimum eigenfrequency of the body. This is achieved using a classical SIMP-like model to approximate the constitutive parameters of the micro-polar medium, whereas an ad hoc penalization is introduced for both the linear and the spin inertia to avoid the occurrence of undesired local modes. The robustness of the proposed procedure is investigated through numerical examples, and the mechanical features of the results obtained are also discussed for a wide range of material parameters. The numerical simulations show that the results are quite sensitive to the material characteristic length and the spin inertia term. The achieved layouts may differ significantly from conventional Cauchy-based solutions.

KEY WORDS: topology optimization, Cosserat media, optimal dynamic response.

Paper No. 102 CV2

Condoleo P., Taliercio A.

STRUCTURAL INVESTIGATION ON THE BASILICA OF SANTA MARIA NOVELLA (in Italian) Proc. Workshop on “Design for rehabilitation of masonry structures” (WONDERmasonry 2011), P. Spinelli & A. De Luca (Eds.), Firenze, November 10-11, 2011, pp. 160-169.

The present work describes the preliminary results of structural analyses carried out on a finite element model of the Basilica of Santa Maria Novella in Florence, aiming at assessing the current conditions of the Basilica and interpreting the surveyed crack pattern. The information gathered in a previous survey campaign (exact geometry of the vaults, crack, and out-of-plumb of the columns and the walls) were employed to define a numerical model that matches the salient features of the real geometry of the Basilica, despite some simplifying assumptions. So far, linear elastic analyses taking only the self-weight of the structural elements into account, were carried out. Despite these limitations, the faults observed in the vaults of the lateral naves and in the perimeter of the transept could be explained. The agreement between numerical predictions and cracks detected in other parts of the Basilica, such as the vaults of the central nave and the transversal walls above this nave, is less satisfactory. Future analyses will include the effects of ground settlements and the out-of-plumb of the pillars of the central nave.

KEY WORDS: Santa Maria Novella, geometric survey, crack pattern, finite elements.

Paper No. 103 RV1

Veber D., Taliercio A.

TOPOLOGY OPTIMIZATION OF THREE-DIMENSIONAL NON-CENTROSYMMETRIC MICROPOLAR BODIES Structural and Multidisciplinary Optimization, Vol. 45, No. 4, pp. 575-587, 2012.

54

The topology optimization problem for linearly elastic micropolar solids is dealt with. The constituent materials are supposed to lack in general of centro-symmetry, which means that force stresses and microcurvatures are coupled, and so are couple stresses and micropolar strains. The maximum global stiffness is taken as objective function. According to the SIMP model, the constitutive tensors are assumed to be smooth functions of the design variable, that is, the material density. Optimal material distributions are obtained for several significant three-dimensional cases. The differences respect to the optimal configurations obtained with classical Cauchy materials and centrosymmetric materials are pointed out. The influence of the constants defining the non-centrosymmetric behaviour on the optimal configurations is discussed.

KEY WORDS: topology optimization, micropolar materials, Cosserat elasticity, chirality.

Paper No. 104 RV1

Bruggi M., Taliercio A.

MAXIMIZATION OF THE FUNDAMENTAL EIGENFREQUENCY OF MICRO-POLAR SOLIDS THROUGH TOPOLOGY OPTIMIZATION Structural and Multidisciplinary Optimization, Vol. 46, No. 4, pp. 549-560, 2012.

Aim of this work is the maximization of the fundamental eigenfrequency of 2D bodies made of micropolar (or Cosserat) materials using a topology optimization approach. A classical SIMP–like model is used to approximate the constitutive parameters of the micropolar medium. A suitable penalization is introduced for both the linear and the spin inertia of the material, to avoid the occurrence of undesired local modes. The robustness of the proposed procedure is investigated through numerical examples; the influence of the material parameters on the optimal material layouts is also discussed. The optimal layouts for Cosserat solids may differ significantly from the truss–like solutions typical of Cauchy solids, as the intrinsic flexural stiffness of the material can lead to curved beam-like material distributions. The numerical simulations show that the results are quite sensitive to the material characteristic length and the spin inertia.

KEY WORDS: topology optimization, Cosserat media, optimal dynamic response.

Paper No. 105 CV1

Ramalho M.A., Taliercio, A.

CLAY BLOCK PRISMS UNDER COMPRESSIVE LOADS: TESTING AND MODELING Proc. 15th Int. Brick & Block Masonry Conference (15th IB2MaC), June 4-6, 2012, Florianòpolis (Brazil), paper 1A2, 10 pp. (CD ROM).

This paper presents a comparison between the results of experimental and

55

numerical analyses of clay block prisms under compression loads. The main goal of the study is to simulate the nonlinear mechanical response of the prisms, based on the behaviour of blocks and mortar joints, using a numerical non-local damage model specifically developed for quasi-brittle materials. An experimental program, with simple compression tests with displacement control, was carried out to determine the damage parameters for the individual components to characterize the numerical model. Prisms were also tested in simple compression to obtain their complete load-displacement diagrams to failure. Despite the simplicity of the experimental procedure, the obtained results show that the damage model employed is able to predict the strength of the prisms reasonably well, as well as their behaviour in the softening regime.

KEY WORDS: masonry, compression, testing, damage, finite element.

Paper No. 106 CV1

Bruggi M., Milani G., Taliercio A.

OPTIMAL FIBER REINFORCEMENT FOR MASONRY STRUCTURES VIA TOPOLOGY OPTIMIZATION Proc. of the Eleventh International Conference on Computational Structures Technology (CST2012), B.H.V. Topping (Editor), Dubrovnik (HR), September 4-7, 2012, paper #235, 13 pp. (USB key).

A novel approach for the optimal positioning of fibre-reinforcements in masonry structures is presented, based on topology optimization techniques. Topology optimization has already been used to generate energy-based truss-like layouts that may be straightforwardly interpreted as strut-and-tie models in concrete structures. The minimization of the so-called structural compliance allows optimal load paths to be defined, which may inspire a safe disposal of steel bars, provided that the structural element is sufficiently ductile. Due to the brittle behaviour of masonry, the minimization of the strain energy cannot be adopted as an objective. The problem may be conveniently re-formulated as a minimization of the amount of reinforcement required to keep tensile stresses in any masonry element below a prescribed threshold. The strength criteria employed for masonry elements are formulated according to a recently presented lower bound limit analysis homogenization model, based on a discretization of a quarter of any unit cell by six CST elements. As a result of the limited number of variables involved, closed form solutions for the masonry macroscopic strength domain can be obtained. This calls for the adoption of a multi-constrained discrete formulation that locally controls the stress field over the whole design domain. The contribution discusses preliminary numerical results addressing fibre-reinforcement of some benchmark masonry walls.

KEY WORDS: masonry, fibre-reinforcement, topology optimization.

56

Paper No. 107 CV1

Casolo S., Milani G., Sanjust C.A., Taliercio A., Maggioni G.

THE SEISMIC BEHAVIOUR OF MANIACE CASTLE, SYRACUSE: A FIRST NUMERICAL COMPARISON BETWEEN THE CURRENT CONDITION AND A HYPOTHETICAL COMPLETE RECONSTRUCTION Proc. 15th World Conference on Earthquake Engineering, Lisbon, September 24-28, 2012, 10 pp. (CD ROM).

The seismic behaviour of Maniace Castle, built on the Ortigia island in Syracuse (Italy) during the thirteenth century by Emperor Frederick II, was investigated by a numerical approach with the aim of comparing different strategies for structural reinforcement. The original building consisted of a square perimeter made by 4 m thick limestone masonry walls and round towers at the corners, embedding a large hypostyle hall. The roof of this main hall was supported by a system of arches, five on each side span. The current state of the castle is the result of subsequent interventions following the explosion that devastated the interior of the castle in 1704. Accordingly, at present the indoor hall consists of only 2/5 of the original covered area, and the primitive structural concept has greatly changed, since the double symmetry of the plant was substantially lost. Buttresses and transverse walls were added to improve the mechanical response to horizontal loads. Previous studies, both experimental and numerical, proved that the interior columns supporting the arches experience a level of vertical stress that is quite high in comparison to the actual strength. The situation is particular serious accounting for the seismicity of Syracuse, as a the significant increase in axial stress in the columns due to their flexural deformation might occur. In the present study, the behaviour of the castle is studied by means of a detailed full 3D FE model, both under vertical and lateral loads. The results of the analysis are used for a proposal of reconstruction of the hypostyle hall, bringing it back to the original geometrical configuration of the XIII century, by the use of modern building materials.

KEY WORDS: masonry, full 3D FE analyses, case study, seismic actions, gravity loads.

Paper No. 108 CV1

Bruggi M., Milani G., Taliercio A.

DESIGN OF THE OPTIMAL FIBER REINFORCEMENT FOR MASONRY STRUCTURES VIA TOPOLOGY OPTIMIZATION Proc. 8th Int. Conf. on Structural analysis of historic constructions (SAHC 2012), Wroklaw (PL), October 15-17, 2012, J. Jasienko (Ed.), Vol. 2, pp. 1789-1796.

The optimal layout of the fiber reinforcement to be placed on existing masonry structures is determined using topology optimization. The problem can be conveniently formulated as the minimization of the amount of reinforcement required to keep tensile stresses in any masonry element below a prescribed

57

threshold. Strength criteria for masonry elements are provided by means of a recently presented lower bound limit analysis homogenization model, relying upon a discretization of one-fourth of the unit cell by six CST elements. The macroscopic strength domain of masonry can be obtained in closed form, thanks to the limited number of variables involved. A multi-constrained discrete formulation that locally controls the stress field over the whole design domain is adopted. The contribution presents some preliminary numerical results addressing the fiber-reinforcement of a benchmark masonry wall.

KEY WORDS: cloister vault, hollow bricks, steel, geometrical survey, numerical modeling.

Paper No. 109 RV2

Casolo S., Milani G., Sanjust A., Taliercio A.

MANIACE CASTLE IN SYRACUSE, ITALY: COMPARISON BETWEEN PRESENT STRUCTURAL SITUATION AND HYPOTHETICAL ORIGINAL CONFIGURATION BY MEANS OF FULL 3D FE MODELS The Open Civil Engineering Journal, Vol. 6, Suppl. 1-M6, pp. 173-187, 2012.

The Maniace Castle in Syracuse, Italy, built under Emperor Frederick II in the first half of the 13th century, is analyzed from a structural point of view by means of a detailed 3D Finite Element model. The castle was struck by many catastrophic events during the centuries, which heavily damaged the structure and caused subsequent changes in the original implant. After a concise description of the main architectural characteristics of the building and its actual state of degradation, two full 3D FE numerical analyses are discussed, representing respectively the present geometric configuration and that obtained after a hypothetical intervention aimed at reporting the structure into its original conceived shape. Conventional static analyses in the linear range are performed on such large scale meshes, under gravity loads and horizontal loads conventionally representing seismic excitation, respectively investigating the role played by self-weight into the degradation of some structural elements (particularly central columns of the hypostyle hall) and the effect induced by horizontal forces on both the global behavior and the local widespread local regions with positive stresses. On the basis of such numerical results, some useful observations to be considered in a future plan of restoration aimed at reporting the castle in its original configuration are finally provided.

KEY WORDS: masonry, full 3D FE analyses, case study, seismic actions, gravity loads.

Paper No. 110 RV1

Bruggi M., Taliercio A.

TOPOLOGY OPTIMIZATION OF THE FIBER-REINFORCEMENT

58

RETROFITTING EXISTING STRUCTURES Int. J. Solids Structures, Vol. 50, No. 1, pp. 121-136, 2013.

The paper presents a numerical approach for the optimal design of any unidirectional fiber-reinforcement to improve the structural performance of existing structural elements. A problem of topology optimization is formulated, simultaneously searching for the regions to be strengthened and the optimal pointwise inclination of the reinforcement. Aim of the formulation is the minimization of the maximum equivalent stress in the underlying material, for a prescribed amount of fiber-reinforcement. The Tsai-Wu failure criterion is implemented to detect highly tensile-stressed regions in the existing structural components, both in case of isotropic material (e.g. concrete) and orthotropic media (e.g. brickwork or reinforced concrete). A suitable set of relaxed stress constraints is dealt with, calling for a no-compression stress state in the fiber-reinforcement. The resulting multi-constrained min-max problem is solved by mathematical programming. Numerical examples are presented to discuss the features of the achieved optimal layouts, along with their possible application as preliminary design for structural retrofitting. Performances of the adopted computational procedure are investigated as well.

KEY WORDS: topology optimization, fiber-reinforcement, orthotropic materials, Tsai-Wu failure criterion, stress constraints, min-max problems.

Paper No. 111 RV1

Bruggi M., Milani G., Taliercio A.

DESIGN OF THE OPTIMAL FIBER-REINFORCEMENT FOR MASONRY STRUCTURES VIA TOPOLOGY OPTIMIZATION Int. J. Solids Structures, Vol. 50, No. 13, pp. 2087-2106, 2013.

A novel approach for the rational positioning of fiber reinforcements on masonry structures based on topology optimization is presented. Due to the brittle behavior of masonry, the minimization of the strain energy cannot be implemented to generate truss-like layouts that may be interpreted as strut-and-tie models in the discontinuity regions of reinforced concrete structures. To cope with the brittleness of brickwork, the optimal problem can be conveniently reduced to the minimization of the amount of reinforcement required to keep tensile stresses in any masonry element below a prescribed threshold. A strength criterion recently proposed for masonry is employed, based on a lower bound limit analysis homogenization model (Milani, 2011) and relying upon a discretization of 1=4 of any unit cell by six CST elements. Thanks to the limited number of variables involved, closed form solutions for the masonry macroscopic strength domain can be obtained. This criterion is implemented into the multi-constrained discrete formulation of the topology optimization algorithm, to locally control the stress field over the design domain. For comparison, the phenomenological Tsai–Wu strength criterion for anisotropic solids is also implemented. The contribution discusses three sets of numerical

59

results, addressing the fiber-reinforcement of some benchmark masonry walls. The optimal reinforcement layouts are found to be affected by the choice of the masonry strength criterion only to a limited extent, as far as failure in the masonry element is mainly due to tensile stresses. Contrary to intuition, placing the reinforcing fibers along the direction of the principal tensile stresses in masonry is also found to be not necessarily the most effective solution, for certain geometries and load conditions.

KEY WORDS: masonry, fiber-reinforcement, topology optimization.

Paper No. 112 CV1

Bruggi M., Cinquini C., Taliercio A.

TOPOLOGY OPTIMIZATION OF MASONRY BLOCKS WITH ENHANCED THERMOMECHANICAL PERFORMANCES Proc. 10th Int. Conf. on World Congress on Structural and Multidisciplinary Optimization (WCSMO-10), Orlando, FL (USA), May 19-24, 2013, paper #5173, 6 pp. (USB key).

Topology optimization is employed to define the geometry of the cross-section of any masonry block that minimizes its thermal transmittance, with the aim of maximizing the thermal insulation of masonry buildings. Constraints on the mechanical properties of the block are also prescribed. The effect of the design constraints on the optimal layout of the blocks is investigated. The thermal efficiency of the optimized units is also compared with that of commercially available blocks.

KEY WORDS: block masonry, thermal conductivity, topology optimization.

Paper No. 113 CV1

Bruggi M., Taliercio A.

OPTIMAL DESIGN OF THE FIBER-REINFORCEMENT TO STRENGTHEN EXISTING STRUCTURES Proc. 10th Int. Conf. on World Congress on Structural and Multidisciplinary Optimization (WCSMO-10), Orlando, FL (USA), May 19-24, 2013, paper #5262, 7 pp. (USB key).

An original approach is proposed to define the optimal design of any unidirectional fiber–reinforcement to improve the structural performance of existing structural elements. A problem of topology optimization is formulated, simultaneously searching for the regions to be strengthened and the optimal local fiber orientation. The maximum equivalent stress in the underlying material is minimized, for a given amount of reinforcement. The Tsai–Wu strength criterion is employed, to take into account the different strength properties of the material in tension and compression and the possible material anisotropy. Tensile stresses

60

along the fiber direction are not allowed in the reinforcement. The resulting multi–constrained min–max problem is solved by mathematical programming. A numerical example is presented to discuss the features of the achieved optimal layouts, along with their possible application to the preliminary design of any fiber reinforcement.

KEY WORDS: topology optimization, fiber-reinforcement, orthotropic materials, Tsai-Wu failure criterion, min-max problems.

Paper No. 114 RV1

Taliercio A.

ANALYSIS OF THE BEHAVIOR OF BRICK MASONRY WITH CALCIUM SILICATE UNITS UNDER SUSTAINED LOADS Masonry International, Vol. 26, No. 1, pp. 17-26, 2013.

The numerical modeling of the time evolution of stresses and strains in brickwork made with Ca2SiO4 units under sustained loads is dealt with, within the framework of linear viscoelasticity. The research aims at investigating the influence of the brick pattern on the creep behavior (global deformation; stress redistribution) of any wall under typical load conditions, and at assessing whether a simplified 2D layered model can be employed to get reliable predictions. To this end, finite element analyses were carried out, using two 3D models representative of header bond masonry and Flemish bond masonry; the results were compared with those given by the layered model. The influence of the mortar properties on the stress redistribution was also investigated. Whereas the layered model provides a fairly good prediction of the global creep deformation for both masonry textures under vertical (uniform and eccentric) load, it cannot be applied under more complex load conditions. Under uniform vertical load, 3D models taking the real masonry pattern into account must be used to predict the local stress evolution accurately. The uncertainties regarding the mortar Poisson’s ratio basically affect the time evolution of the transversal stress in the units and the joints.

KEY WORDS: masonry, creep, linear viscoelasticity, header bond, Flemish bond.

Paper No. 115 CV1

Ramalho M.A., Taliercio A.

NUMERICAL AND EXPERIMENTAL ANALYSIS OF CRACKS AND FAILURE MODE OF CONCRETE BLOCK PRISMS Proc. 12th Canadian Masonry Symposium, Vancouver, BC (Canada), June 2-5, 2013, paper #565, 11 pp. (USB key).

This paper presents a comparison between experimental and numerical analysis of concrete block prisms under compressive loads. The main goal of the study is

61

to compare damage obtained using a numerical non-local damage model specially developed for quasi-brittle materials with the cracks observed in an experimental program. First, blocks and mortar specimens are submitted to compression and direct tension tests in order to identify their damage parameters. Then, prisms are also tested to evaluate their behavior. All the tests are carried out with displacement control to obtain the complete load-displacement diagram for the specimens: the initial linear behavior, the failure load and the post-peak softening branch. After the experimental program, numerical models are developed, using eight-node ‘brick’ finite elements with secant stiffness matrix. An increasing displacement is applied to the model to simulate the tests. Finally, the cracks and failure mode obtained experimentally are compared with a scalar measure of the damage obtained with the numerical models. Obtained results show that the nonlocal damage model considered in this paper is able to predict the cracks and even the failure mode of the prisms observed in the experiments.

KEY WORDS: structural masonry, prisms, compression, damage model.

Paper No. 116 CV1

Cecchi A., Taliercio A.

CREEP BEHAVIOUR OF BRICKWORK: A PARAMETRIC INVESTIGATION Proc. 14th Int. Conf. on Civil, Structural and Environmental Engineering Computing (CC2013), B.H.V. Topping and P. Iványi, (Eds.), Cagliari, 3-6/9/13, paper #76, 15 pp. (USB key).

The prediction of the creep behavior of periodic brickwork subjected to in-plane loads is dealt with. Analytical approximate expressions for the macroscopic relaxation and creep coefficients are proposed, according to simple statically or kinematically admissible solutions in which the joint thickness is neglected, units are assumed to be either rigid or elastic, and creep phenomena are confined in the interfaces between units. A parametric analysis is carried out to investigate the effect of several parameters on the global and local creep behavior of brickwork, namely: i) mortar-to-brick thickness ratio; ii) ratio of the mortar Young's modulus to the brick Young's modulus; iii) brickwork texture (running vs header bond). A FE model of a single Representative Volume Element (RVE) is also analyzed under sustained macroscopic stresses, to numerically evaluate the creep coefficients and assess the accuracy of the analytical estimates. The creep coefficients are found to be very sensitive to the block stiffness for thin joints. Also, the agreement between numerical and analytical predictions is as better as thicker the mortar joints are.

KEY WORDS: masonry, creep, viscoelasticity, periodicity, homogenization.

Paper No. 117 CV1

Bruggi M., Taliercio A.

62

MINIMIZATION OF THE THERMAL TRANSMITTANCE OF MASONRY BLOCKS BY TOPOLOGY OPTIMIZATION Proc. 14th Int. Conf. on Civil, Structural and Environmental Engineering Computing (CC2013), B.H.V. Topping and P. Iványi, (Eds.), Cagliari, 3-6/9/13, paper #150, 15 pp. (USB key).

A contribution toward the thermal insulation of masonry buildings is given, assuming the heat flux across any wall to be uniform along its height and seeking the optimal geometry of the cross-section of any block forming the wall. The minimization of the thermal transmittance of the block is dealt with as a Topology Optimization problem. Constraints on the mechanical properties of the block are also prescribed, to allow for the presence of in-plane and out-of-plane loads. A parametric investigation is carried out to investigate the effects of the design constraints and the geometry of the boundary of the block on their optimal layout. The thermal efficiency of the optimized units is also compared with that of standard blocks, showing that topology optimization may be conveniently adopted to improve the thermo-mechanical performances of conventional layouts.

KEY WORDS: thermal transmittance, thermal insulation, masonry, block, topology optimization.

Paper No. 118 CV1

Bruggi M., Milani G., Taliercio A.

OPTIMAL REINFORCEMENT FOR MASONRY WALLS SUBJECT TO TWO-WAY BENDING Proc. 14th Int. Conf. on Civil, Structural and Environmental Engineering Computing (CC2013), B.H.V. Topping and P. Iványi, (Eds.), Cagliari, 3-6/9/13, paper #82, 14 pp. (USB key).

In this paper, the problem of finding the optimal layout of the reinforcement for out-of-plane loaded masonry walls is dealt with by a topology optimization approach. The layout of the reinforcing layers that minimizes the structural compliance (i.e., that maximizes the structural stiffness) for a given amount of reinforcement is sought, using a multi-constrained topology optimization algorithm. The reinforcement is assumed to be placed symmetrically on both sides of the wall. The proposed approach is applied to the determination of the optimal reinforcement of solid and windowed panels. The increase in stiffness given by the numerically predicted reinforcement layout compared with the unreinforced panels is pointed out.

KEY WORDS: masonry, reinforcement, out-of-plane loads, topology optimization, minimum compliance, SIMP.

63

Paper No. 119 CV2

Cecchi A., Taliercio A.

A COMPARISON BETWEEN NUMERICAL AND ANALYTICAL HOMOGENIZED MODELS FOR VISCO-ELASTIC BRICKWORK Atti XXI Congresso AIMETA di Meccanica Teorica e Applicata, Torino, 17-20/9/2013, 10 pp. (CD Rom).

The creep behaviour of periodic brickwork is dealt with. An analytical model is proposed, in which units are assumed to be either rigid or elastic and creep effects are confined to mortar joints. Closed-form expressions for the creep coefficients under elementary macroscopic stresses are obtained. A parametric study is carried out to investigate the sensitivity of the analytical creep coefficients to the material parameters. The accuracy of the theoretical predictions and the reliability of the simplifying assumptions is assessed through comparisons with the numerical results obtained discretizing any representative volume element by finite elements and taking the creep behavior of both component materials (bricks and mortar) into account. Experimental data available in the literature for calcium silicate bricks and mortar were used to calibrate the model. The analytical creep coefficients are found to be accurate as the ratio of the elastic modulus of the units to the elastic modulus of mortar is greater than 20.

KEY WORDS: homogenization, analytical model, finite elements, visco-elasticity, masonry.

Paper No. 120 CV2

Bruggi M., Taliercio A., Cinquini C.

ANALYSIS OF NO-TENSION BODIES THROUGH A TOPOLOGY OPTIMIZIATION APPROACH Atti XXI Congresso AIMETA di Meccanica Teorica e Applicata, Torino, 17-20/9/2013, 10 pp. (CD Rom).

An alternative numerical approach is presented for the analysis of no-tension masonry-like solids. Whereas most of the strategies available in the literature resort to non–linear finite element techniques, the proposed approach re-formulates the problem within the framework of topology optimization. The equilibrium of a two–dimensional no-tension body is found searching for the distribution of an equivalent orthotropic material, in which tensile principal stresses are not allowed by prescribing negligible stiffness in the relevant direction, such that the potential energy of the solid is minimized. Unlike many conventional approaches that deal with the inherent non-linearity of the problem through step-wise incremental analyses, the proposed energy-based method efficiently solves the effect of compatible loads through a single optimization run. Analytical and numerical benchmarks from the literature are investigated to assess the effectiveness of the proposed procedure.

64

KEY WORDS: no-tension materials, topology optimization, orthotropic materials.

Paper No. 121 RV1

Bruggi M., Taliercio A.

DESIGN OF MASONRY BLOCKS WITH ENHANCED THERMOMECHANICAL PERFORMANCES BY TOPOLOGY OPTIMIZATION Construction and Building Materials, Vol. 48, pp. 424-433, 2013.

The problem of maximizing the thermal insulation of buildings is dealt with, by determining the geometry of masonry blocks that minimizes the transmittance of any wall. Assuming the heat flux to be uniform across the wall surfaces, topology optimization is employed to define the layout of the block section. Constraints on the block stiffness are also prescribed. The presence of holes of given shape in any prescribed position and other technological constraints can be easily embodied in the optimization procedure. The effect of the design constraints on the optimal layout of the blocks is investigated. The thermal efficiency of the optimized units is also compared with that of commercially available blocks.

KEY WORDS: block masonry, thermal conductivity, topology optimization.

Paper No. 122 RV2

Bruggi M., Milani G., Taliercio A.

DESIGN OF THE OPTIMAL FIBER REINFORCEMENT FOR MASONRY STRUCTURES VIA TOPOLOGY OPTIMIZATION Wiadomosci Konserwatorskie - Journal of Heritage Conservation, No. 34, pp. 23-27, 2013.

The optimal layout of the fiber reinforcement to be placed on existing masonry structures is determined using topology optimization. The problem can be conveniently formulated as the minimization of the amount of reinforcement required to keep tensile stresses in any masonry element below a prescribed threshold. Strength criteria for masonry elements are provided by means of a recently presented lower bound limit analysis homogenization model, relying into a discretization of one-fourth of the unit cell by six CST elements. The macroscopic strength domain of masonry can be obtained in closed form, thanks to the limited number of variables involved. A multi-constrained discrete formulation that locally controls the stress field over the whole design domain is adopted. The contribution presents some preliminary numerical results addressing the fiber-reinforcement of a benchmark masonry wall.

KEY WORDS: masonry, fiber-reinforcement, topology optimization.

65

Paper No. 123 RV1

Bruggi M., Milani G., Taliercio A.

SIMPLE TOPOLOGY OPTIMIZATION STRATEGY FOR THE FRP REINFORCEMENT OF MASONRY WALLS IN TWO-WAY BENDING Computers & Structures, Vol. 138, pp. 86-101, 2014.

A multi-constrained topology optimization approach is employed to define the layout of the reinforcing layers that minimizes the structural compliance (i.e. that maximizes the structural stiffness) of retrofitted out-of-plane loaded masonry walls, for a given amount of reinforcement. The reinforcement is supposed to be symmetrically placed on both sides of the wall. The macroscopic elastic properties of brickwork in bending are derived through an original homogenization approach, which relies upon the discretization of 1/4 of any unit cell by six CST elements. Topology optimization is then applied to the determination of the optimal reinforcement of solid and windowed panels. The increase in stiffness given by the numerically predicted reinforcement layout respect to the unreinforced panels is pointed out.

KEY WORDS: masonry, reinforcement, out-of-plane loads, topology optimization, minimum compliance, SIMP.

Paper No. 124 RV1

Taliercio A.

CLOSED-FORM EXPRESSIONS FOR THE MACROSCOPIC ELASTIC AND CREEP COEFFICIENTS OF BRICK MASONRY Int. J. Solids Structures, Vol. 51, No. 17, pp. 2949-2963, 2014.

Approximate expressions for the macroscopic in-plane elastic and creep coefficients of brick masonry with a regular pattern are derived in closed form, using a homogenization approach for periodic media. A microscopic displacement field fulfilling suitable periodicity boundary conditions, and depending on a limited number of degrees of freedom, is formulated over any masonry Representative Volume Element (RVE). According to this field, closed-form expressions for the macroscopic elastic constants are obtained at various degrees of approximation, either using a Method of Cells-type approach, or minimizing the potential energy of the RVE subjected to any given macroscopic stress. Eventually, the results are extended to the description of the global creep behavior of brickwork under service loads, assuming the creep laws of units and mortar to be expressed by Prony series. Using the FE solution as a benchmark, the proposed approach is found to accurately match both the macroscopic constitutive law in linear elasticity and the time evolution of the macroscopic strains of brickwork under sustained macroscopic stress.

KEY WORDS: masonry, homogenization, finite elements, elasticity, visco-elasticity, macroscopic moduli.

66

Paper No. 125 CV1

Bruggi M., Taliercio A.

FIBER-REINFORCEMENT OF CONCRETE PLATES THROUGH TOPOLOGY OPTIMIZATION Proc. Int. Conf. on Engineering and Applied Sciences Optimization (OPT-i), Kos (GR), June 4-6, 2014, M. Papadrakakis, M.G. Karlaftis, N.D. Lagaros (Eds.), paper #3246, 10 pp. (CD Rom).

The achievement of an optimal arrangement of fiber-reinforcement is a crucial issue for the efficient retrofitting of concrete elements. Numerical approaches to the automatic optimal design of fiber–reinforced polymers (FRPs) have been recently proposed in the literature to address in–plane loaded structural elements, such as beams and shear walls. Combining topology optimization techniques with methods typical of the so called free material design, a mathematical problem can be formulated that searches for the best distribution of a given amount of unidirectional FRP along with its optimal orientation, with the aim of maximizing any objective function. Dealing with concrete slabs subjected to lateral loads, the reinforcing layers to be applied on the two sides of the element are usually different. Modeling the slab through plate finite elements, the contribution of each layer to the local stiffness matrix is shown to depend on a density field and an orientation field. Accordingly, the proposed procedure defines the layout of the layers that minimizes the overall strain energy of the reinforced structure, computing the optimal values of four unknown design variable fields. Indeed, this choice for the objective function is suggested by technical codes when performing the automatic research of load paths for the design of reinforced structural elements, see the case of strut–and–tie methods. A suitable set of stress constraints is introduced to penalize any compressed FRP element. This turns out to be an effective technique to achieve a distribution of no–compression reinforcement, as required in practice. The discrete setting is solved through mathematical programming. Numerical investigations are presented to discuss the features of the computed optimal layouts, along with the possible application as preliminary design for the structural retrofitting of concrete slabs. The obtained layouts are compared with solutions suggested by limit analysis theory, which suggests to reinforce plates perpendicularly to the hinges arising in the unreinforced elements. The performances of the adopted computational procedure are investigated as well.

KEY WORDS: topology optimization, fiber-reinforcement, concrete slabs, orthotropic materials, unilateral materials.

Paper No. 126 CV1

Taliercio A.

A METHOD OF CELLS-TYPE APPROACH TO ESTIMATE THE MACROSCOPIC ELASTIC AND CREEP COEFFICIENTS OF BRICK MASONRY Proc. 9th Int. Masonry Conf., Guimarães (P), July 7-9, 2014, paper # ID 857, 12 pp.

67

(USB key).

The problem of obtaining reliable analytical expressions for the macroscopic elastic and creep coefficients of brick masonry with a regular pattern according to the mechanical properties of the individual constituents (e.g. mortar and units) is dealt with. Starting from the microscopic displacement field estimated over any Representative Volume Element by a refined finite element model with suitable periodicity boundary conditions, a kinematic solution is proposed that depends on a limited number of degrees of freedom and matches the numerical predictions with fair accuracy. According to this field, the macroscopic constitutive law is derived in closed form at various degrees of approximation. A minimization of the potential energy of the RVE under any macroscopic stress respect to all the model d.o.f.s is shown to give values for the macroscopic elastic constants in excellent agreement with the FE results taken as a benchmark. Eventually, the results are extended to the description of the global creep behaviour of brickwork under service loads, assuming both units and mortar to obey Zener rheological model. Using the concept of effective modulus, the proposed approach is found to accurately predict also the macroscopic delayed moduli of brickwork given by the FE model.

KEY WORDS: masonry, brickwork, homogenization, elasticity, creep.

Paper No. 127 RV2

Bruggi M., Milani G., Taliercio A.

OPTIMAL FRP REINFORCEMENT OF MASONRY WALLS UNDER IN- AND OUT-OF-PLANE LOADS Proc. 4th Int. Seminar on Mechanics of Masonry Structures Strengthened with Composite Materials (MuRiCo4), Ravenna (I), September 9-11, 2014, pp. 429-436. (also published in Key Engineering Materials, Vol. 624, pp. 429-436, 2015).

The problem of finding the optimal layout of FRP strips to effectively retrofit masonry walls undergoing transverse loads is dealt with, taking the presence of permanent vertical loads into account. An innovative topology optimization approach is proposed to define the minimum amount of reinforcement that keeps the stress within a given strength domain throughout the wall. The macroscopic strength properties of masonry are defined by means of a simplified limit analysis approach based on homogenization theory. The capabilities of the proposed procedure are illustrated through applications on a windowed panel subjected to out-of-plane actions and vertical loads.

KEY WORDS: masonry, FRP strengthening, homogenization, limit analysis, topology optimization.

68

Paper No. 128 CV1

Bruggi M., Milani G., Taliercio A.

OPTIMAL FIBER REINFORCEMENT OF MASONRY WALLS LOADED OUT-OF-PLANE Proc. 9th Int. Conf. on Structural Analysis of Historic Constructions (SAHC 2014), F. Peña & M. Chávez (eds.), October 14-17, 2014, Mexico City, 12 pp. (e-book ISBN 04-2014-102011495500-102).

The problem of the optimal external reinforcement with FRP strips of masonry walls under lateral loads is dealt with, by means of a combined homogenization-topology optimization approach. A homogenization procedure is utilized to deduce both the orthotropic elastic moduli of masonry and the out-of-plane strength domain. The elastic moduli are estimated by minimizing the total complementary energy of any discretized elementary cell. The out-of-plane failure surface is numerically evaluated by means of the lower bound theorem of limit analysis. Joints are reduced to interfaces obeying a Mohr-Coulomb strength criterion with tension cut-off and a cap in compression. For bricks, a classic Mohr-Coulomb criterion is employed. The out-of-plane macroscopic strength domain is deduced by integration of the stresses along the thickness. The optimization problem is written assuming perfect bonding between FRPs and masonry, meaning that a fiber-reinforced layer is modelled as an additional contribution to the out-of-plane stiffness of the underlying brickwork. Constraints on the internal actions in masonry are also imposed at any Gauss point. The proposed approach is applied to the determination of the optimal reinforcement of a rectangular panel. The numerically predicted optimal layout is compared with that given by an energy-based approach, in which the stiffness of the panel is maximized for a given amount of reinforcement.

KEY WORDS: masonry, homogenization, out-of-plane loads, limit analysis, topology optimization, stress constraints.

Paper No. 129 CL1

Bruggi M., Taliercio A.

TOPOLOGY OPTIMIZATION FOR THE DEVELOPMENT OF ECO-EFFICIENT MASONRY UNITS in ‘Eco-efficient Masonry Bricks and Blocks’, F. Pacheco-Torgal, P.B. Lourenço, J.A. Labrincha, S. Kumar & P. Chindaprasirt (Eds.), Woodhead Pub., Cambridge (UK), Chap. 19, pp. 425 - 445, 2015, ISBN 978-1-782423-05-8.

The shape of the cross-section of hollow blocks that maximizes the thermal insulation of masonry buildings is sought, by minimizing the thermal transmittance of any wall. The heat flux across the wall surfaces is supposed to be uniform along the wall height, so that the problem can be formulated as 2D. Topology optimization is employed to define the layout of the block section, prescribing constraints on the block stiffness under in-plane and out-of-plane

69

loads. Blocks of square or rectangular cross-section, either with flat or indented sides, are considered in the applications. The influence of the design constraints and the geometry of the boundary on the optimal layout of the blocks is numerically investigated. The decrease in thermal transmittance of the optimized units compared to commercially available blocks can be extremely significant (down to -30%, depending on the prescribed constraints). Accordingly, the proposed formulation seems to be a promising candidate for the design of thermally efficient masonry blocks.

KEY WORDS: block masonry, thermal conductivity, topology optimization.

Paper No. 130 RV1

Milani G., Taliercio A.

IN-PLANE FAILURE SURFACES FOR MASONRY WITH JOINTS OF FINITE THICKNESS ESTIMATED BY A METHOD OF CELLS-TYPE APPROACH Computers & Structures, Vol. 150, pp. 34-51, 2015.

The macroscopic strength domain of in-plane loaded masonry walls is derived using an approach based on the upper bound theorem of limit analysis within the framework of homogenization theory. Following an approach similar to the Method of Cells for fiber-reinforced composites, a typical representative volume of masonry is subdivided into a few sub-cells, and a strain-rate periodic, piecewise differentiable velocity field, depending on a limited number of degrees of freedom, is defined. The ensuing approximated macroscopic failure surface is found to match with fair accuracy both available experimental data and theoretical predictions obtained by other authors with more refined numerical approaches. The proposed model is also applied to the prediction of the bearing capacity of a deep masonry beam: for any joint thickness, the criterion is found to give results as accurate as other complex numerical models, which take the heterogeneous nature of masonry into account. The model thus combines computational efficiency and accuracy.

KEY WORDS: masonry, in-plane loads, homogenization, macroscopic strength, Method of Cells (MoC), Upper Bound Limit Analysis (UBLA).

Paper No. 131 RV1

Bruggi M., Taliercio A.

OPTIMAL STRENGTHENING OF CONCRETE PLATES WITH UNIDIRECTIONAL FIBER-REINFORCING LAYERS Int. J. Solids Struct., Vol. 67-68, pp. 311-325, 2015.

The problem of the optimal strengthening of concrete plates subjected to transverse loads by unidirectional FRP layers is dealt with. A topology optimization (TO) procedure is proposed to define the layout of the layers that

70

maximizes the elastic stiffness of the reinforced plate for a given maximum amount of reinforcing material. The anisotropy of the layers is taken into account, and local orientations of the fibers are included in the set of design variables. According to the SIMP model for TO problems, the mechanical properties of the reinforcing layers are assumed to depend locally on the densities of the material in the layers, which are additional design variables. Compressive stresses along the fibers are avoided by a suitable penalization technique. The possibility of cracking in the concrete core is also indirectly taken into account. The discretized version of the constrained minimization problem that gives the optimal solution is solved by mathematical programming, using the Method of Moving Asymptotes and the finite element method in its displacement-based formulation. Numerical investigations are presented to discuss the features of the computed optimal layouts, along with the possible application as preliminary design for the structural retrofitting of concrete plates. The reliability of the achieved layouts is also investigated comparing the distribution and orientation of the reinforcing fibers with the yield lines that characterize the collapse mechanisms of the analyzed concrete plates suggested by limit analysis theory. The good performances of the adopted numerical procedure are also pointed out. It follows that the proposed procedure is a robust and computationally effective tool for the preliminary design of the optimal reinforcement of concrete plates in bending.

KEY WORDS: topology optimization, concrete plates, fiber-reinforcement, energy-based problems, orthotropic materials, unilateral materials, yield lines.

Paper No. 132 RV1

Bruggi M., Taliercio A.

ANALYSIS OF NO-TENSION STRUCTURES UNDER MONOTONIC LOADING THROUGH AN ENERGY-BASED METHOD Computers & Structures, Vol. 159, pp. 14-25, 2015.

An approach is proposed to estimate the collapse load of linear elastic isotropic no-tension 2D solids. The material is replaced by a suitable equivalent orthotropic material with spatially varying local properties. A non-incremental energy-based algorithm is implemented to define the distribution and the orientation of the equivalent material, minimizing the potential energy so as to achieve a compression-only state of stress. The algorithm is embedded within a numerical procedure that evaluates the collapse mechanisms of structural elements under monotonic loading. The accuracy of the method is assessed through comparisons with the ‘‘exact’’ results predicted by limit analysis.

KEY WORDS: energy-based methods, no-tension materials, masonry-like bodies, collapse mechanisms, structural optimization.

71

Paper No. 133 CV1

Bruggi M., Taliercio A.

ANALYSIS OF MASONRY VAULTS AS A TOPOLOGY OPTIMIZATION PROBLEM Proc. 3rd Int. Conf. on Mechanical Models in Structural Engineering (CMMoST 2015), June 24-16, 2015, Sevilla (E), pp. 91-100 (USB Key)

An innovative approach is proposed to analyze 3D masonry vaults, assuming masonry to behave as a linear elastic no-tension material. Masonry is replaced by a suitable equivalent orthotropic material with spatially varying elastic properties and negligible stiffness in any direction along which tensile stresses must be prevented. An energy-based algorithm is implemented to define the distribution and the orientation of the equivalent material for a given load, minimizing the potential energy so as to achieve a purely compressive state of stress. The algorithm is embedded within a numerical procedure that performs a non-incremental analysis under given loads. The collapse load of masonry structural elements can also be predicted running a sequence of independent analyses. The capabilities of the approach in predicting the crack pattern in typical masonry vaults are also shown.

KEY WORDS: masonry vaults, linear elasticity, no-tension material, FEM, topology optimization.

Paper No. 134 CV1

Milani G., Taliercio A.

A METHOD OF CELLS-TYPE APPROACH TO PREDICT THE MACROSCOPIC STRENGTH OF MASONRY WALLS IN TWO-WAY BENDING Proc. 15th Int. Conf. on Civil, Structural and Environmental Engineering Computing (CC2015), J. Kruis, Y. Tsompanakis and B.H.V. Topping (Eds.), Prague, September 1-4, 2015, paper #62, 15 pp. (USB key).

Following an approach recently presented by the authors to estimate the in-plane homogenized failure surfaces of masonry walls with joints of finite thickness, in this paper an extension is proposed to predict the macroscopic strength properties of walls subjected to out-of-plane loads. Similarly to the so-called method of cells for fiber-reinforced composites, a typical representative volume is subdivided into a few sub-cells, and a strain-rate periodic, piecewise differentiable velocity field, depending on a limited number of degrees of freedom, is defined. Upper bounds to the macroscopic strength domain of the wall in the space of the macroscopic bending and twisting moments are obtained by applying the kinematic theorem of limit analysis within the framework of homogenization theory for periodic media. By means of standard linear mathematical programming, several points of the approximated macroscopic failure surface are determined, each one representing an upper bound to the ultimate load bearing capacity of the wall under given moment combinations.

72

The approximated macroscopic failure surfaces are in good agreement with those previously obtained, at a much higher computational cost, by alternative numerical approaches.

KEY WORDS: masonry, homogenization, transverse loads, limit analysis, upper bound.

Paper No. 135 CV1

Bruggi M., Taliercio A.

FINITE ELEMENT ANALYSIS OF MASONRY VAULTS THROUGH A 3D NO-TENSION APPROACH Proc. 15th Int. Conf. on Civil, Structural and Environmental Engineering Computing (CC2015), J. Kruis, Y. Tsompanakis and B.H.V. Topping (Eds.), Prague, September 1-4, 2015, paper #67, 14 pp. (USB key).

Assuming masonry to behave as a linear elastic no-tension material, an original approach is proposed to analyze three-dimensional masonry structural elements, with special attention to masonry vaults. Masonry is replaced by a suitable equivalent orthotropic material with spatially varying elastic properties. Using an interpolation typical of topology optimization, the stiffness of the equivalent material is given negligible values in any direction along which tensile stresses must be prevented. An energy-based algorithm is implemented to define the distribution and the orientation of the equivalent material for a given load, so as to obtain a purely compressive state of stress throughout the element. The collapse load of masonry structural elements can also be predicted running a sequence of independent analyses. The capabilities of the approach in predicting no-tension stress solutions in masonry vaults of different shape is shown.

KEY WORDS: masonry, vaults, linear elasticity, no-tension material, finite element, topology optimization.

Paper No. 136 CV2

Bruggi M., Taliercio A.

FIBER-REINFORCEMENT OF CONCRETE PLATES BY TOPOLOGY OPTIMIZATION Memorie estese XXII Congresso AIMETA di Meccanica Teorica e Applicata, Genova, 14-17/9/2015, pp. 109-118 (http://aimeta2015.dicca.unige.it/), ISBN 978-88-97752-55-4

Topology optimization is employed to define the optimal layout of fiber-reinforced layers to be applied on concrete plates subjected to transverse loads in order to maximize their elastic stiffness, for a given amount of reinforcing material. The mechanical properties of the reinforcing material are assumed to depend on their local density, according to the so-called SIMP model. Both the

73

density and the orientation of the reinforcing material are design variable fields. Compressive stresses along the fibers are avoided by a suitable penalization technique. The possibility of cracking in the concrete core is also indirectly taken into account. Some numerical examples illustrate the capability of the proposed approach in defining reinforcing layouts that spontaneously resist the failure mechanisms of the unreinforced plate predicted by limit analysis.

KEY WORDS: topology optimization, fiber-reinforcement, concrete plates.

Paper No. 137 CV2

Milani G., Taliercio A.

MACROSCOPIC STRENGTH DOMAINS OF TRANSVERSALLY LOADED MASONRY WALLS DEFINED BY A METHOD OF CELLS-TYPE APPROACH Memorie estese XXII Congresso AIMETA di Meccanica Teorica e Applicata, Genova, 14-17/9/2015, pp. 430-439 (http://aimeta2015.dicca.unige.it/), ISBN 978-88-97752-55-4

The paper generalizes an upper-bound limit analysis approach, recently presented by the authors to estimate the in-plane homogenized failure surfaces of masonry walls with joints of finite thickness, to walls subjected to lateral loads. Following an approach similar to the Method of Cells for fiber-reinforced composites, a typical representative volume is subdivided into a few sub-cells, and a piecewise differentiable velocity field perpendicular to the element mid-plane, depending on a limited number of degrees of freedom and fulfilling suitable periodicity conditions, is proposed. Approximated macroscopic failure surfaces in the space of the macroscopic bending and twisting moments are obtained in the framework of the kinematic theorem of limit analysis. By means of standard linear programming, different points of the approximated failure surface are determined, each one representing an upper bound to the ultimate load bearing capacity of the wall under given moment combinations. The upper bounds to the macroscopic failure surfaces are found to match well, at a reduced computational cost, those obtained with previously presented alternative numerical approaches.

KEY WORDS: masonry, transverse loads, macroscopic strength, Method of Cells.

Paper No. 138 CV2

Taliercio A.

A METHOD OF CELLS-TYPE APPROACH FOR THE DETERMINATION OF THE MACROSCOPIC ELASTIC OUT-OF-PLANE COEFFICIENTS OF MASONRY Memorie estese XXII Congresso AIMETA di Meccanica Teorica e Applicata, Genova, 14-17/9/2015, pp. 440-449 (http://aimeta2015.dicca.unige.it/), ISBN 978-88-97752-55-4

74

The macroscopic bending and twisting stiffness coefficients of masonry walls with a regular brick pattern are derived in closed form, according to a Method of Cells-type approach recently proposed to estimate the in-plane macroscopic moduli of brickwork. A Representative Volume Element (RVE) is divided into a few sub-cells, and the microscopic transverse displacement field is discretized by a piecewise-differentiable expression depending on very a limited number of parameters and fulfilling suitable periodicity conditions. By averaging the moment and curvature fields over the RVE, the macroscopic flexural rigidity of the wall can be estimated. Using the FE solution of a masonry panel subjected to elementary load conditions as a benchmark, the proposed approach is found to accurately match the numerically obtained stiffness coefficients, for panels of different geometry and different mechanical properties.

KEY WORDS: masonry, homogenization, transverse loads, Method of Cells.

Paper No. 139 RV1

Taliercio A., Veber D.

TORSION OF ELASTIC ANISOTROPIC MICROPOLAR CYLINDRICAL BARS Eur. J. Mech. A/Solids, Vol. 55, pp. 45-56, 2016.

The effects of a torque on a cylindrical bar, either solid or hollow, made of an anisotropic micropolar linear elastic material are analyzed. The elastic properties are supposed to be invariant along the cylinder axis. One of the principal directions of the material elasticity tensors is parallel to the cylinder axis; the other two are arbitrarily rotated in the plane of any cross-section of the bar. Closed-form, approximate solutions are obtained if the material internal length is much smaller or much larger than the cylinder outer radius; the latter solution applies for particular orientations of the material symmetry axes. In the general case, only numerical solutions of the governing equations can be derived. A parametric study is carried out on the effect of different parameters (material internal length, orientation of the symmetry axes, etc.) on the stress distribution and the torsional rigidity of the cylinder. The size effects associated with the material internal length are pointed out in terms of torsional rigidity, both for solid and hollow cylinders.

KEY WORDS: linear elasticity, cylinder, size effects.

Paper No. 140 RV1

Milani G., Taliercio A.

LIMIT ANALYSIS OF TRANSVERSALLY LOADED MASONRY WALLS USING AN INNOVATIVE MACROSCOPIC STRENGTH CRITERION Int. J. Solids Struct., Vol. 81, pp. 274-293, 2016.

The macroscopic strength properties of masonry walls with joints of finite

75

thickness subjected to out-of-plane loads are estimated following an approach similar to the so-called Method of Cells for fiber-reinforced composites. A typical representative volume is subdivided into a few sub-cells, and a strain-rate periodic, piecewise differentiable transverse velocity field, depending on a limited number of degrees of freedom, is defined. Upper bounds to the macroscopic strength domain of the wall in the space of the macroscopic bending and twisting moments are obtained by applying the kinematic theorem of limit analysis within the framework of homogenization theory for periodic media. The approximated macroscopic failure surfaces are in good agreement with the ‘exact’ ones, available in the literature for infinitely strong units and infinitely thin joints, and with those obtainable by accurate 2D and 3D numerical models, at a much higher computational cost, for units of limited strength and joints of finite thickness. The influence of compressive in-plane loads and of the joint thickness on the macroscopic out-of-plane strength of the wall is also numerically investigated. Finally, the proposed model is applied to the prediction of the bearing capacity of laterally loaded masonry elements: the accuracy of the numerical predictions is assessed by comparisons with available experimental results and with more refined numerical models proposed by other authors.

KEY WORDS: masonry, homogenization, transverse loads, Method of Cells, limit analysis.

Paper No. 141 RV1

Taliercio A.

CLOSED-FORM EXPRESSIONS FOR THE MACROSCOPIC FLEXURAL RIGIDITY COEFFICIENTS OF PERIODIC BRICKWORK Mech. Res. Comm.., Vol. 72, pp. 24-32, 2016.

Approximate expressions for the macroscopic out-of-plane elastic coefficients of brick masonry with a regular pattern are derived in closed form using a homogenization approach for periodic media. Following an approach similar to the Method of Cells for fiber reinforced composites, a (piecewise-)differentiable expression depending on very a limited number of degrees of freedom and fulfilling suitable periodicity conditions is proposed for the microscopic transverse displacement field over any Representative Volume Element (RVE). Some of the equilibrium conditions at the interfaces between bricks and mortar joints are also fulfilled. By averaging the moment and curvature fields over the RVE, the macroscopic bending stiffness coefficients can be explicitly obtained. Using the FE solution of a masonry panel subjected to elementary load conditions as a benchmark, the proposed approach is found to accurately match the numerically obtained stiffness coefficients, for masonry elements of different geometry and different mechanical properties. In several instances, the proposed expressions agree with the numerical predictions better than other analytical expressions available in the literature.

KEY WORDS: masonry, homogenization, macroscopic stiffness, transverse loads, out-

76

of-plane.

Book No. 1 LA1

Taliercio A.

COURSE OF STRUCTURAL MECHANICS II (in Italian) Ed. Libreria CLUP, Milano, ISBN 88-7090-531-4, 356 pp., 2002.

This textbook covers topics which are usually dealt with in degree courses of Advanced Structural Mechanics at Politecnico di Milano. Basically, the textbook consists of two parts. In the first one, the fundamentals of Solid Mechanics are revised, with particular emphasis on the role of the Virtual Work equation in Structural Mechanics and energy formulations of the linear elastic problem. Then, plane problems of elasticity are analyzed and some structural (or engineering) theories for beams and plates in bending are discussed. Finally, the fundamentals of the Finite Element Method in linear elasticity are presented; the characteristics of some of the most widely employed elements for the analysis of two- and three-dimensional solids, frames and plates are illustrated. In the second part, the behaviour is first described of materials which can be modeled as elastic-perfectly plastic and of beams consisting of such materials. Then, the non-linear step-by-step analysis of elastic-plastic frames is approached and the concept of collapse mechanism is introduced. Finally, the fundamentals are shown of the classical Limit Analysis, which allows the load-bearing capacity of ideally plastic structures to be directly estimated, providing insofar engineers with a powerful tool to design and analyze structures.

KEY WORDS: solid mechanics, elasticity, two-dimensional problems, beams, plates, Finite Element Method, plasticity, limit analysis.

Book No. 2 LA1

Taliercio A.

MECHANICS OF BEAM SYSTEMS (in Italian) Ed. Esculapio, Bologna, ISBN 88-7488-194-0, 271 pp., 2005.

The textbook deals with the study of plane systems of beams (including frame structures, which are widely employed in civil buildings), both in terms of stress analysis and in terms of displacement evaluation. The study is restricted to the linear elastic field. The last part of the book tackles the stability analysis of compressed beams. The textbook is addressed to degree courses in Engineering and Architecture (such as Structural Mechanics, Strength of Materials, etc.) where Mechanics of beam systems and Solid Mechanics are independently dealt with. The presentation is accompanied by a number of solved exercises, at the

77

end of each chapter.

KEY WORDS: beams, trusses, frames, elastica, virtual work, strain energy, buckling.

Book No. 3 LA1

Corigliano A., Taliercio A.

COMPUTATIONAL MECHANICS: SOLUTION OF THE LINEAR ELASTIC PROBLEM (in Italian) Ed. Esculapio, Bologna, ISBN 88-7488-188-6, 406 pp., 2005.

The book gives an overview of the main techniques for the solution of the linear elastic problem, with particular reference to the Finite Element Method. The first part is devoted to the formulation of the linear elastic problem for three-dimensional, axisymmetric and bi-dimensional continua and to the discussion of beam and plates structural theories. Some meaningful cases are analytically solved. In the second part of the book, the Finite Element Method is introduced starting from a general formulation for deformable solids. The book gives all the information necessary to the full understanding of the FEM and to its application for the analysis of linear elastic solids and structures.

KEY WORDS: computational mechanics, linear elastic problem, Finite Element Method.

Book No. 4 LA1

Taliercio A.

INTRODUCTION TO SOLID MECHANICS (in Italian) Ed. Esculapio, Bologna, ISBN 88-7488-171-1, 317 pp., 2006.

The textbook aims at providing readers with the theoretical bases for the evaluation of the deformation and the stress state within any linearly elastic solid and the assessment of its admissibility. Special attention is devoted to the “Saint-Venant’s solid”, which constitutes a reasonable approximation of a beam. The theoretical treatment is followed by several solved problems at the end of each section. Also, closed-form solutions are presented of some elasticity problems useful in engineering practice.

KEY WORDS: solid mechanics, stress, strain, linear elasticity, strength criteria, Saint-Venant’s problem.