Proceedings of the 23rd International Congress of Theoretical and Applied MechanicsEditors：Yilong Bai , Jianxiang Wang , Daining Fang

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Preface

The idea of ICTAM originated from a conference on hydrodynamics andaerodynamics held in Innsbruck in 1922. It was at this conference thatTheodore von Karman suggested that an international congress might be heldto cover the whole field of applied mechanics. This led to the firstInternational Congress of Applied Mechanics held in Delft in 1924, organizedby J. M. Burgers and C. B. Biezeno, where the Executive Committee madethe decision to constitute a permanent institution – the International Congressfor Applied Mechanics. During the sixth Congress in Paris, it was proposedthat the Congress of Applied Mechanics should transform itself into a Union.Thus, the IUTAM was founded in 1946. The term “theoretical” has beenadded to the official names of the Congresses since the thirteenth Congress,though theoretical mechanics has always been an essential part of theCongresses.

This International Congress of Theoretical and Applied Mechanics(ICTAM2012) held in Beijing constitutes the twenty-third one of the ICTAMseries. The recent decades have witnessed remarkable evolution of mechanics

August 19 - 24 , 2012Beijing , China

Organized by

The International Union of Theoretical

and Applied Mechanics (IUTAM)

Hosted by

The Chinese Society of Theoretical and

Applied Mechanics (CSTAM)

Preface

Technical Program

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from major classical branches and applications to many interdisciplinary areasinteracting with environmental science, biology, materials science andtechnology, geophysics, energy technology, etc. The papers contributed to thisCongress reflect recent achievements in fundamental understanding ofdeformation and motion of matter, in applications of mechanics to moderntechnology, and in education in mechanics. Thus, we hope it fulfills theobjective of ICTAM, that is, to bring together scientists from all over theworld to exchange information on recent developments in the field ofmechanics to advance research, application and education in mechanics.

This 23rd International Congress of Theoretical and Applied Mechanics ishosted by The Chinese Society of Theoretical and Applied Mechanics(CSTAM). The preparation of the Congress involves the devotion andcontribution of many organizations, institutions and individuals. On behalf ofthe organizer, we thank all the contributors to this Congress and hope youenjoy the meeting in Beijing.

Yilong Bai

Jianxiang Wang

Beijing, August, 2012

Contents

IUTAM Congress Committee

Chinese Steering Committee

Local Organizing Committee

Acknowledgements

The International Union of Theoretical and Applied Mechanics

The Chinese Society of Theoretical and Applied Mechanics

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Proceedings of the 23rd International Congress of Theoretical and Applied MechanicsEditors：Yilong Bai , Jianxiang Wang , Daining Fang

Navigation: Home >>Members of the IUTAM Congress Committee

Members of the IUTAM Congress Committee

● Nadine Aubry USA

● Yilong Bai China Member of XCCC (ex officio)

● Leslie Banks-Sills Israel

● Dominique Barthès-Biesel France

● Martin Bendsøe Denmark Member of XCCC

● Dick van Campen The Netherlands Member of XCCC

● Alberto Carpinteri Italy

● Gengdong Cheng China

● Renato Cotta Brazil

● Frederic Dias France

● Peter Eberhard Germany

● Bruno Eckhardt Germany

● Irina Goryacheva Russia

● Narinder Gupta India

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● GertJan van Heijst The Netherlands

● Carl Herakovich USA

● Yukio Kaneda Japan

● Tomasz Kowalewski Poland Member of XCCC

● Stelios Kyriakides USA

● Pierre Ladevèze France

● Gary Leal USA

● Jean-Baptiste Leblond France

● Jacques Magnaudet France

● Robert McMeeking USA

● Nikita Morozov Russia

● Ray Ogden UK

● Nigel Peake UK

● Timothy Pedley UK President of IUTAM, President of XCCC

● Krishnaswamy Ravi-Chandar USA

● Gábor Stépán Hungary

● Howard Stone USA

● Kazuo Tanishita Japan

● André Thess Germany

● Viggo Tvergaard Denmark Member of XCCC

● Genki Yagawa Japan

XCCC: Executive Committee of the Congress Committee of IUTAM

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Proceedings of the 23rd International Congress of Theoretical and Applied MechanicsEditors：Yilong Bai , Jianxiang Wang , Daining Fang

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Contents

PL01：Opening LecturePL02：Closing LecturePL03：G. K. Batchelor Prize LecturePL04：Rodney Hill Prize Lecture

Sectional Lectures

Mini-symposia

MS01：Mechanical challenges in energyMS02：Mechanics of natural disastersMS03：Fluid-structure interactions in biological systemsMS04：Mechanics of transport in microfluidic devicesMS05：Dynamics and control of morphing structuresMS06：Effects of small size scales in materials modeling

Pre-Nominated Sessions (Fluid Mechanics)

FM01：Biological fluid dynamics

August 19 - 24 , 2012Beijing , China

Organized by

The International Union of Theoretical

and Applied Mechanics (IUTAM)

Hosted by

The Chinese Society of Theoretical and

Applied Mechanics (CSTAM)

Preface

Technical Program

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FM02：Boundary layersFM03：Combustion and flamesFM04：Compressible flowFM05：ConvectionFM06：Drops, bubbles and multiphase flowsFM07：Flow instability and transitionFM08：Flow in thin filmsFM09：Geophysical and environmental fluid dynamicsFM10：Low Reynolds number flowFM11：MagnetohydrodynamicsFM12：Non-Newtonian and complex fluidsFM13：Stirring and mixingFM14：TurbulenceFM15：Vortex dynamicsFM16：Waves in fluidsFM17：General fluid mechanics

Pre-Nominated Sessions (Solid Mechanics)

SM01：Biomechanics and biomaterialsSM02：Contact and friction mechanicsSM03：Damage mechanicsSM04：ElasticitySM05：Fracture mechanicsSM06：Geophysics and geomechanicsSM07：Impact mechanics and wave propagationSM08：Mechanics of multi-component materials and compositesSM09：Mechanics of phase transformationsSM10：Mechatronics

Contents

IUTAM Congress Committee

Chinese Steering Committee

Local Organizing Committee

Acknowledgements

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SM11：Multibody and vehicle dynamicsSM12：Nanostructures and MEMSSM13：Plasticity, viscoplasticity and creepSM14：Stability of structuresSM15：Structural optimization (Co-sponsored by ISSMO)SM16：Vibrations and control of structuresSM17：General Solid Mechanics

Pre-Nominated Sessions(Topics involving both Fluid Mechanics and Solid Mechanics)

FS01：AcousticsFS02：Computational methods in mechanicsFS03：Experimental methods in mechanicsFS04：Chaos and pattern formationFS05：Electro- and magnetomechanical systemsFS06：Fluid structure interactionsFS07：Smart materialsFS08：Granular materials and flowsFS09：Mechanics of materials processingFS10：Porous mediaFS11：Foams and cellular materialsFS12：Education in mechanics

The International Union of Theoretical and Applied Mechanics

The Chinese Society of Theoretical and Applied Mechanics

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Proceedings of the 23rd International Congress of Theoretical and Applied MechanicsEditors：Yilong Bai , Jianxiang Wang , Daining Fang

Navigation: Home >> Mechanics of multi-component materials and composites

Mechanics of multi-component materials and composites

Numbering Thesis Name Joint Author

SM08-003The route to simultaneous high stregnth and highductility metals through engineered nanocrystallineinterlayers

X. Guo, G.J. Weng, A.K. Soh

SM08-005 Damage propagation of composite materialreinforced by randomly-dispersed particles Jiaoyan Li, James Lee, Ken Chong

SM08-007 Three-dimensional cryomechanics analysis of satinwoven carbon/polymer composites with cracks Fumio Narita, Yasuhide Shindo, Tomo Takeda

SM08-009 Failure analysis of composites by a component-wiseapproach

Erasmo Carrera, Marianna Maiaru, MarcoPetrolo

SM08-010 Local buckling of sandwich materials withnon-orthogonal plain woven composite facesheets Long Du, XiaoJun Huang, Bin Ye

SM08-011 Investgation on transient heat transfer of 3d braidedcomposites Suyang Zhong, Licheng Guo

SM08-012 Optimal design for hybrid composites under flexuralloading Chensong Dong, Ian J. Davies

SM08-013Necessary conditions and approximate self-consistentestimates for the overall creep function ofviscoelastic heterogeneous materials

Renald Brenner, Pierre Suquet

SM08-015 Periodic structural solids and composites: mechanicsand multifunctional applications Lifeng Wang

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SM08-016 Modelling of anisotropic composites by newlydeveloped HFS-FEM Changyong Cao, Qinghua Qin, Aibing Yu

SM08-017 Chiral effect in planar isotropic micropolar elasticity Xiaoning Liu, Guoliang Huang, Hu Gengkai

SM08-019 Bounds on the effective elastic moduli of three-phasecomposites with coated spherical inclusions Linzhi Wu

SM08-020 Damage detection in CFRP bolted joints usingembedded optical fiber strain distribution monitoring Nobuo Takeda, Shu Minakluchi, Takeaki Nadabe

SM08-021Three-dimensional piezoelasticity solution for hybridpiezoelectric laminated plates featuring viscoelasticinterfaces

Amit Kumar, Santosh Kapuria, N. K. Gupta

SM08-022Synthesis and formation mechanism of carbon-encapsulated copper nanoparticles in detonationprocess

Ning Luo, Kaixin Liu, Xiaojie Li

SM08-027 Stress-strain curve of a fiber network Svetlana Borodulina, Artem Kulachenko, MikaelNygards

SM08-028 Modeling of compressive strength of z-pinned fibercomposites with the distorted fiber arctecture Junqian Zhang, Shunli Xie

SM08-030 Micromechanics of fiber-crack interaction: bridgingfiber Zhenkun Lei, Quan Qang, Wei Qiu, Libo Deng,

SM08-031 Electromechanical transition in a dielectric elastomer:giant linear deformation and failure modes

Jian Zhu, Zhigang Suo, Matthias Kollosche,Guggi Kofod

SM08-032 Optimization of magnetoelectric effect in multiferroiccomposites Hsin-Yi Kuo, Yongliang Wang, Yumin Kuo

SM08-034 On viscoelastic properties of three-dimensionallybraided composites Huiyu Sun, Yongming Cai

SM08-038 Tuning electromagnetic properties of metamaterialsby mechanical deformation Shengqiang Cai, Nicholas Fang

SM08-039 Upper and lower limits in the elastic properties oflow-shrink sheet molding compounds Horatiu Teodorescu-Draghicescu, Sorin Vlase

SM08-040 Analysis of effective properties of composites by theboundary element method

Piotr Fedelinski, Radoslaw Gorski, GrzegorzDziatkiewicz, Jacek Ptaszny

SM08-041 Micromechanics governing the undulation patterns ofinter-cellular boundaries of plant epidermis cells Yaning Li, Narges Kaynia, Mary C. Boyce

SM08-045Modeling of composites with different physical andgeometrical connectivities by effective modules andfinite element methods

Andrey V. Nasedkin

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SM08-048

Stress-strain relation of bi2sr2cacu2ox/agmgsuperconducting round wires based on fractalcharacterization of the rough surfaces of individualfilaments

Xiaofan Gou, Justin Schwartz

SM08-050 Advances in the comprehension of the mechanicalbehavior of steel corrosion products

Anita Dehoux, Yves Berthaud, FatihaBouchelaghem

SM08-051 Micromechanics-based modeling of porous materialsfor application to elasto-plastic indentation analysis Roland Traxl, Roman Lackner

SM08-052 Collapse mechanisms of a blast-resistant uhmwpecomposite beam

Norman A. Fleck, G. Liu, Vikram S.Deshpande,Michael D. Thouless

SM08-053 Quasi-static indentation tests on closed-cell Al foam Xinzhu Wang, Xianghe Peng, Zaoyang Guo

SM08-054Numerical study on the effects of equi-biaxialresidual stress on mechanical Properties of Nickelfilm by means of nanoindentation

Shiguo Long, Lizeng Ling, Zengsheng Ma, XuLiang

SM08-055 Multifunctional nano-tailored composites for in situself-health monitoring of aircraft structures Jacob M. Wernik, Shaker A. Meguid

SM08-057Steel short fiber reinforced concrete (SFRC) strengthand post cracking behaviour appreciation by fibersmotion prediction in fresh concrete during casting

Andrejs Krasnikovs, Olga Kononova, ArtursMachanovskis, Vitalijs Lusis

SM08-060 A higher order solution for cylindrical bendingvibrations of functionally graded plates Sandeep Shiyekar, Tarun Kant

SM08-062 A unified constitutive model for interface debondingand friction Irene Guiamatsia, Giang D. Nguyen

SM08-064 Modeling failure mechanisms of 3D orthogonalinterlock hybrid textile composites in flexure Dianyun Zhang, Anthony Waas, Chian Yen

SM08-065 Mesomechanical model of reticulate CNT/polymercomposites to bridge atom and continuum scales Qingsheng Yang, Xia Liu

SM08-066

The statistical second-order two-scale analysis forThermo-elastic coupled performance of thecomposite structure with consistent randomdistribution of grains

Zihao Yang, Junzhi Cui

SM08-067A micromechanical model for the effectiveviscoelastic response of semi-crystallinepolymer-clay nanocomposites

Kokou Anoukou, Fahmi Zairi, Gregory Stoclet,Moussa Nai-Abdelaziz, Ali Zaoui, Jean-MichelGloaguen, Jean-Marc Lefebvre

SM08-068 Influence of friction between the contacting phasesof the fiber composite on its stress-strain condition Halina M. Kuziomkina, Volha I. Yakubovich

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XXIII ICTAM, 19-24 August 2012, Beijing, China

MODELLING OF ANISOTROPIC COMPOSITES BY NEWLY DEVELOPED HFS-FEM

Changyong Cao

*, Qinghua Qin

* a) & Aibing Yu

** *Research School of Engineering, Australian National University, Canberra, ACT 0200, Australia

**School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia

Summary In this work anisotropic composite is modeled efficiently and accurately by a newly proposed hybrid finite element method

based on Green’s functions. The hybrid method is formulated based on two independent assumptions: intra-element field covering the

element domain and inter-element frame field along the element boundary. A modified functional, which satisfies the governing equation,

boundary and continuity conditions between elements, is proposed to derive the element stiffness. In this work, the foundational solutions

of anisotropic materials derived from the elegant and powerful Stroh formalism are employed to approximate the intra-element

displacement field of the elements, while the polynomial shape functions used in traditional FEM are utilized to interpolate the frame

field. Numerical results show that the proposed method is accurate and efficient in modeling anisotropic composite, and can be easily

extended to analyze composite laminates with good accuracy.

INTRODUCTION

In materials science, composite laminates are usually assemblies of layers of fibrous composite materials which can be

joined to provide required engineering properties, such as in-plane stiffness, bending stiffness, strength, and coefficient

of thermal expansion [1]. In the viewpoint of micromechanics, the fiber and matrix of each lamina can be treated as the

inclusion and matrix, respectively, while from the viewpoint of macromechanics, each lamina can be treated as

anisotropic or orthotropic materials and the laminates can be dealt as a general anisotropic body by classical lamination

theory. Hence, the analysis of anisotropic bodies is important for understanding of the micro- or macro-mechanical

behavior of composites [1]. Stroh formalism [2, 3], which has been shown to be elegant and powerful, is widely used to

find the analytical solutions for anisotropic problems [2]. However, numerical methods such as FEM and BEM are

usually resorted to solve more complex problems with complicated boundary constraints and loading conditions. In this

paper a new hybrid finite element formulation (HFS-FEM) for anisotropic composite has been developed based on the

associated fundamental solutions derived from Stroh formalism. As an alternative to the Hybrid Trefftz-FEM, this new

method inherits the advantages of the HT-FEM over the FEM and the BEM, such as high accuracy using coarse meshes,

insensitivity to mesh distortion, great liberty in element shape, and accurately representing various local effects [4]. It is

of interest to develop a uniform framework in HFS-FEM to solve anisotropic and isotropic problems together.

DEVELOPMENT OF THE METHODOLOGY

In the Cartesian coordinate system (x1, x2, x3), if we neglect the body force ib , the equilibrium equations, the stress-

strain laws and the strain-displacement equations of for anisotropic elasticity are [2]

, ,, ( ) / 2 0, , , 1,2 , 3ij j iij i jjkl kl i j j iC e e u u i j (1)

where ij is the stress tensor,

kle the strain tensor, ijklC the fourth-rank anisotropic elasticity tensor, and iu the

displacement vector. To solve the anisotropic problem governed by Eq. (1) using HFS-FEM approach, the solution

domain has to be divided into a series of elements as done in conventional FEM. For each element, two

independent fields, i.e. intra-element field and frame field, are assumed in a manner as that presented in [5]. In this

approach, the intra-element field u(x) and the frame field ( )u x for a particular element e are approximated as

( , ), ( ) ( )e sj e e e e e e

u(x) N c x y u x N d x , (2)

where the matrix e

N is composed by the fundamental solution * ( , )ij sju x y , which is obtained by the Stroh formalism as

ˆˆIm ln /z z Tu A A p [2], and unknown vector 11 21 31 1 2 3[ ]T

n n nc c c c c ce

c ,eN is the matrix of

shape functions, ed is the nodal displacements of elements. It is noted that the source point sjy for the fundamental

solution calculations are placed outside the element to avoid the singularity encountered as in BEM. In the above,

complex variable 1 2z x p x , 1,2,3 , p are material eigenvalues with positive imaginary part, 1 2 3

A = a ,a ,a

and 1 2 3B = b ,b ,b are 3×3 complex matrices composed by the material eigenvector matrix associated with p . In

the absence of the body forces, the hybrid functional me for a particular element e is constructed as

1( )

2 e t eme ij ij i i i i id t u d t u u d

(3)

a) Corresponding author. Email: qinghua.qin@anu.edu.au.

XXIII ICTAM, 19-24 August 2012, Beijing, China

where the boundary e of the element is

e eu et eI , and where ,eu e u et e t and eI is the

inter-element boundary of element e. Using Gaussian theorem and equilibrium equations, the stationary condition of the

functional me with respect to ce and de, respectively, yields the stiffness equation

e e eK d = g , where the sparse

element stiffness matrix 1

e e e e

TK = G H G , and T d

ee e e

H Q N , T d

ee e e

G Q N , T

te e d

g N t .The numerical

calculations for eH ,

eG and eg can resort to the popular Gauss integration as used in FEM and BEM.

NUMERICAL EXAMPLES

An irregular composite lamina is modeled to demonstrate the performance of the proposed method in dealing with

composite materials. The material parameters are assumed as El=11.8 GPa, E2=5.9 GPa, G12=0.69 GPa, v12= 0.071.

The geometry of the plate is shown in Fig.1 (a), where L=50 mm and W=50 mm, the semi-major and minor axes of the

elliptical cut are a=2 mm and b=1 mm, respectively. A uniform tension of 0 =1 GPa is applied in 2x direction.

(a) W

L

a

b

0

1x

2x

A

B

o

(b) 0 10 20 30 40 50 60 70 80 90

-2

0

2

4

6

8

10 ABAQUS

HFS-FEM

Ho

op

str

ess

(

GP

a)

Angle (Degree)

(c) 0 10 20 30 40 50 60 70 80 90

0

2

4

6

8

10

12

14

SC

F (/

0)

Angle (Degree)

ABAQUS

HFS-FEM

Fig.1: (a) Irregular composite plate with an elliptic cut; (b) Hoop stresses along the rim of the elliptical cut for different

lamina angle ; (c) Variation of stress concentration factor (SCF) at point A with fiber angle .

Fig. 1 (b) shows the hoop stresses along the rim of elliptical cut for different fiber angle . The relationship between

SCF and fiber angle is described in Fig. 1 (c). It is obvious that the fiber orientation in lamina has a significant

influence on the SCF of the plate. It is also observed that there is a very good agreement between the reference values by

ABAQUS using a very fine mesh and the computed solutions by HFS-FEM on a much coarser mesh (about 1/5 of

ABAQUS). These results indicate the capability of this method in analyzing static problems for anisotropic composite

materials. Fig. 2 shows the contour plots of the stress components around the cut region when fiber angle 45o .

Other important and interesting applications of the method will be presented in detail at the conference.

x

y

0 2 40

2

4

Sigma_11

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

x

y

0 2 40

2

4

Sigma_22

3.6

3.4

3.2

3

2.8

2.6

2.4

2.2

2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

x

y

0 2 40

2

4

Sigma_12

0.2

0

-0.2

-0.4

-0.6

-0.8

-1

-1.2

-1.4

-1.6

-1.8

-2

-2.2

Fig. 2: Contour plots of stress components around the cut region in the composite plate (Lamina angle 045 ).

CONCLUSIONS

A new hybrid finite element method, based on the fundamental solutions derived by Stroh formalism, has been developed to

analyze anisotropic composite materials. Numerical results show that the proposed method is an accurate and efficient

method to analyze various problems involving anisotropic composites, and it can be easily extended to analyze composite

laminates. The detailed techniques involved and other applications of the method will be presented at the conference.

References

[1] Vasiliev, V.V. and E.V. Morozov, Advanced mechanics of composite materials. 2007: Elsevier Science.

[2] Ting, T.C.T., Anisotropic Elasticity: Theory and Applications 1996, NewYork: Oxford Science Publications.

[3] Stroh, A.N., Dislocations and cracks in anisotropic elasticity. Philosophical Magazine, 1958. 3(30): p. 625-646.

[4] Qin, Q.H., The Trefftz finite and boundary element method. 2000, Southampton WIT Press.

[5] Wang, H. and Q.H. Qin, FE approach with green's function as internal trial function for simulating bioheat transfer in the human eye. Archives of

Mechanics, 2010. 62(6): p. 493-510.