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Materials Science and Engineering A 472 (2008) 242–250

Shear behavior of aluminum lattice truss sandwich panel structures

Gregory W. Kooistra, Douglas T. Queheillalt ∗, Haydn N.G. WadleyDepartment of Materials Science and Engineering, University of Virginia, 140 Chemistry Way, Charlottesville, VI 22904, USA

Received 13 February 2007; received in revised form 8 March 2007; accepted 9 March 2007

bstract

Age hardenable 6061 aluminum tetrahedral lattice truss core sandwich panels have been fabricated by folding perforated sheets to form highlyexible cellular cores. Flat or curved sandwich panels can be fabricated by furnace brazing the cores to facesheets. Flat sandwich panels withore relative densities between 2 and 10% have been fabricated and tested in the σ±13 shear orientation (minimum shear strength orientation for aetrahedral lattice) in the fully annealed (O) and aged (T6) conditions. The shear strength of the lattices increased with relative density, parent alloyield strength and work hardening rate. Analytical stiffness and strength predictions agree well with measured values for all relative densities and

arent alloy heat treatments investigated. The stiffness and strength of 6061-T6 aluminum tetrahedral lattice structures are shown to be comparableo those of conventional 5052-H38 aluminum closed cell hexagonal honeycombs and more than 40% stiffer and stronger than flexible honeycombssed for the cores of curved sandwich panels. 2007 Elsevier B.V. All rights reserved.

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eywords: Lattice structures; Sandwich structures; Aluminum alloys; Brazing

. Introduction

Millimeter cell size, aluminum alloy lattice structures witharious open cell topologies are attracting interest as lightweightore structures for sandwich panel constructions. For bendingominated applications of sandwich panels; the facesheets carryhe bending stresses with one facesheet in compression and onen tension and the flexural strength of the panel is governed by thehear response of the core and by the strength of its attachmentoints (nodes) to the facesheets. The core also increases theexural stiffness of the panel by providing a separation between

he two facesheets.Lattices appear to be mechanically competitive alternatives

o prismatic (corrugated) and perhaps honeycomb structureshen configured as the core of a sandwich panel. These lattice

andwich structures are of particular current interest becausef their potential fully open interior structure which facili-ates multifunctional applications [1–4]. For example, lattice

ore sandwich panels appear capable of supporting significanttructural loads while also facilitating cross flow heat exchange5–8]. Some structures also enable high authority shape morph-

∗ Corresponding author. Tel.: +1 434 982 5678; fax: +1 434 982 5677.E-mail address: dougq@virginia.edu (D.T. Queheillalt).

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921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2007.03.034

ng [9–14] and all appear to provide significant high intensityynamic load protection [15–21]. Lattices are also flexible andre amenable to the creation of singly or compound curved sand-ich panels. They may also alleviate some of the delamination

nd corrosion concerns associated with the use of traditionallosed cell honeycomb sandwich panels [22,23].

The emergence of microscale lattice truss structures origi-ally envisioned at the meter scale by Buckminster Fuller [24]as been paced by the development of practical methods for theiranufacture [4,25]. Initial efforts to fabricate millimeter scale

tructures employed investment casting of high fluidity castinglloys such as copper/beryllium [26], aluminum/silicon [27–30]nd silicon brass [27]. However, the tortuosity of the latticesnd ensuing casting porosity made it difficult to fabricate highuality structures at low relative densities (2–10%) identifieds optimal for sandwich panel constructions [31]. While someattice constructions appear to possess significant tolerance toefects such as occasional weak trusses or nodes [32,33], theow toughness of the materials used to make these as-cast lattice

aterials have often lacked the mechanical robustness requiredor the most demanding structural applications [34].

Efforts to exploit the inherent toughness of many wroughtngineering alloys led to the development of alternative latticeabrication approaches based upon perforated metal sheet fold-ng [35]. These folded truss structures can be bonded to each

G.W. Kooistra et al. / Materials Science and

Fig. 1. Comparison between the normalized compressive peak strengths of thealuminum tetrahedral lattice structures and commercially available competingt

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Sandwich panels were constructed from the folded latticestructures by placing them between 6951 aluminum alloy facesheets clad with a 4343 aluminum–silicon braze alloy. The

opologies that utilize aluminum alloys [42].

ther or to facesheets by conventional joining techniques suchs brazing, transient liquid phase (TLP) bonding or weldingechniques to form all metallic lattice truss sandwich panels.anels fabricated from austenitic stainless steels with tetrahe-ral [35–37] and pyramidal lattice truss [38–41] topologiesave been made by node row folding of a patterned sheeto form the core and TLP bonding to facesheets. Because ofhe high temperatures normally encountered with TLP bond-ng, this process results in sandwich panels which remain in aow strength, annealed condition. While these structures appear

uch more robust than their investment cast counterparts, theeduced strength of their annealed microstructure can limit theirotential uses for some structural applications.

The perforated sheet folding method has recently beenxtended to age hardenable aluminium alloys such as the 6061ystem, and tetrahedral lattices made from this alloy have beenhown to exhibit high specific compressive strengths (Fig. 1)42]. Comparisons with other cellular aluminum topologiesFig. 1), confirm that 6061 aluminum alloy tetrahedral latticetructures are far superior to aluminum open cell metal foamsnd prismatic corrugations. The compressive response of theetrahedral lattice was comparable to that of honeycomb panelsf similar specific mass and found to be sensitive to the lat-ices heat treatment condition. Annealed cores with high tangent

oduli were more efficient than age hardened structures and sig-ificantly exceeded elastic-ideally plastic strength predictions.nelastic column-buckling models robustly predict the throughhickness compressive strengths and resolved the important rolef the parent materials post-yield tangent modulus in delayinghe onset of unstable inelastic buckling.

Here, we explore the in-plane shear stiffness and strengthf these 6061 aluminum tetrahedral lattice structures describedbove. The measured shear stiffness and strengths of the lat-ice truss structures are compared to analytical predictions and

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Engineering A 472 (2008) 242–250 243

hown to be comparable to those of other topologies for alu-inum based sandwich structures.

. Fabrication methodology

.1. Tetrahedral lattice truss fabrication

A detailed description of the fabrication approach for mak-ng 6061 aluminum alloy lattice truss structures can be foundn Kooistra et al. [42]. Briefly, a folding process was used toend elongated hexagonal perforated 6061 sheet to create a sin-le layer tetrahedral truss lattice. The folding was accomplishedsing a paired punch and die tool to fold node rows into reg-lar tetrahedrons with three trusses emanating from each nodeesulting in a highly flexible core structure.

The unit cell of a tetrahedral lattice is shown in Fig. 2. Theelative density, ρ̄, of a tetrahedral lattice with 50% occupancyf the available tetrahedral sites is given by ref. [27]:

¯ = 2√3

1

cos2ω sinω

( t

l

)2(1)

here ω is the angle between the truss members and the tetra-edron base plane (ω = 54.7◦ for regular tetrahedrons) and t andare the sheet thickness and truss member length, respectively.he relative density of the lattice was varied here by modifi-ation of the sheet thickness and the perforation dimensions toaintain a square truss cross section and a constant truss length

Table 1).

.2. Sandwich panel fabrication

ig. 2. Tetrahedral unit cell used to derive relative density and mechanical prop-rties. The positive and negative shear directions are also shown. They result inifferent stress–strain behaviors because of the different truss tensile stretchingnd compressive buckling configurations.

244 G.W. Kooistra et al. / Materials Science a

Table 1Predicted and measured relative densities of tetrahedral lattice truss structures

t/l Relative density

ModelEq. (1)

Pre-brazemeasurement

Post-brazemeasurement

0.063 0.017 0.017 ± 0.003 0.020 ± 0.0010.079 0.027 0.025 ± 0.004 0.030 ± 0.0020.099 0.042 0.029 ± 0.004 0.039 ± 0.0010.125 0.067 0.048 ± 0.003 0.069 ± 0.0020.178 0.136 0.083 ± 0.002 0.106 ± 0.003

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ig. 3. Photograph of a tetrahedral lattice truss attached to facesheets by arazing method, ρ̄ = 0.039.

ssemblies were coated with a metal-halide flux and placed in aurnace for brazing in air at 595 ± 5 ◦C for between 5 and 10 min43]. After air-cooling, the samples were solutionized at 530 ◦Cor 60 min and either furnace cooled for the fully annealed (O)ondition or water quenched and aged at 165 ◦C for 19 h for theged (T6) condition [44]. Fig. 3 shows an example of one of theandwich panels with a core relative density, ρ̄ = 0.039.

The nodes of the lattice truss core were ground flat prior torazing to ensure good contact between the lattice core and theace sheets. This resulted in post-braze measurements of the rel-tive densities slightly higher than those predicted by Eq. (1).able 1 summarizes the truss geometries, the measured and pre-icted relative densities. The mean post-braze relative densityreported at a confidence level of 95%) was used to identify theest specimens and for subsequent experimental data normaliza-ions.

Tensile coupons of the 6061 alloy accompanied the coreshrough each thermal process step and were used to deter-

ine the mechanical properties of the parent aluminum alloy inoth the O and T6 tempers. Three tensile tests were performedccording to ASTM E8 at a strain rate of 10−3 s−1for each heatreatment condition [45]. Table 2 shows the mechanical propertyata for 6061 aluminum in the O and T6 tempers.

. Shear experiments

The sandwich panels were tested according to ASTM C273sing a compression shear plate configuration at a nominal strain

ilta

able 2echanical property data for 6061 aluminum in the O and T6 tempers from the uniax

eat treatmentondition

Young’s modulus,Es (GPa)

Yield strengtσys (MPa)

nnealed (O) 68.6 70ged (T6) 69.1 268

nd Engineering A 472 (2008) 242–250

ate 10−3 s−1 at an ambient temperature of 22 ◦C [46]. Thepplied force was used to calculate the stress imparted to theandwich structure, while shear displacement data of the rigidlates was obtained by laser extensometry and the shear strain isimply the displacement divided by the height of the sandwichore.

Initial experiments indicated the need for a rigid bondetween the sandwich panel facesheets and shear plates, espe-ially during evaluation of the highest relative density (strongest)ores. The test samples were attached using four mechanisms torevent premature debonding and/or movement during testing.he grit blasted surfaces were adhesively bonded using an epoxydhesive (Loctite Hysol® E-120HP). The facesheets were alsoastened to the shear plates using steel machine screws. Finally,echanical locking utilizing a leading edge stop machined into

he shear plate and a trailing edge adjustable clamping bar wassed to reduce load transfer stresses.

. Results

Fig. 4a and *b shows representative shear stress–strain behav-or for the annealed and aged samples loaded in theσ+13 directionsee Fig. 2), which corresponds to one truss loaded in compres-ion and the other two in tension (positive orientation). Fig. 4cnd d shows representative shear stress–strain behavior for thennealed and aged samples loaded in the negative σ−13 direc-ion, where one truss member is loaded in tension and the otherwo in compression.

The annealed samples tested in the σ+13 direction (Fig. 4a)ustained large macroscopic shear strains (as high as 35%)ithout rupture of the tensile loaded truss members. For these

amples there was a small linear response during initial loading,ollowed by yielding and increased load support. After largeeformations (which increased with sample relative density)he tensile truss members underwent strain localization (neck-ng) followed by rupture and a decrease in the load support.ig. 5 shows photograph of strain localization in a truss mem-er (at 34.1% macroscopic strain) for an annealed sample with

¯ = 0.069 sample.The aged samples (Fig. 4b) exhibited a better defined linear

lastic region followed by observable plastic yielding of the ten-ile truss members. Load support continued to increase until aeak strength was reached. Initiation of truss member rupturehen coincided with a sharp decrease in its load carrying capac-

ty. These tensile ruptures were observed to occur at variousocations along the truss member length independent of rela-ive density. Fig. 6 shows photographs of an aged sample withrelative density, ρ̄ = 0.039 at various stages of deformation.

ial Cauchy (true) stress–true strain curves

h, Ultimate tensilestrength, σTS (MPa)

Strain at failure,εf (%)

208 21.2306 15.1

G.W. Kooistra et al. / Materials Science and Engineering A 472 (2008) 242–250 245

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ig. 4. Shear stress–strain responses for tetrahedral lattice structures. Represenardened condition and for the σ−13 orientation in the (c) annealed and (d) aged

The annealed shear samples tested in the (negative) σ−13irection (Fig. 4c), also sustained very large macroscopic strains.or these samples there was an initial linear response, followedy yielding and then a period of stably increasing load support.

peak strength was eventually reached, corresponding with the

uckling of the compressively loaded truss members. The agedamples tested in the σ−13 direction (Fig. 4d), also behavedimilarly. However, truss buckling was observed to occur at

ig. 5. Photograph of the ρ̄ = 0.069 annealed tetrahedral lattice truss at a strainevel of 34.1%.

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responses are shown for the σ+13 orientation in the (a) annealed and (b) agedened condition. Note the change in strain axes for the age hardened samples.

significantly lower plastic shear strain consistent with theower tangent modulus of the heat treated condition. Some nodeebonding was observed in the higher relative density sampless indicated in Fig. 4d.

The stiffnesses for both orientations were determined fromnload/reload measurements in the nominally elastic portion ofhe shear stress strain response. There was no effect of loadingirection or heat treatment. Fig. 7 shows a plot of the normalizedhear stiffness, Γ = G/(Esρ̄), where G is the shear modulus ands is the Young’s modulus. The shear modulus measurementshown in Fig. 7 are the average of two experiments conductedor each orientation and heat treatment (eight measurements perelative density) shown. The data indicate a linear dependencef shear modulus upon relative density and is well fitted by aelation of the form: G = 0.11Esρ̄.

The normalized shear 0.2% offset yield strength for the σ±13

rientations for both the annealed and aged samples is plottedersus ρ̄ in Fig. 8. The experimental data for the normalizedield strength of both the annealed and aged cores indicate aild dependence upon relative density for both the positive and

246 G.W. Kooistra et al. / Materials Science a

Fig. 6. Photographs of the ρ̄ = 0.039 T6 tetrahedral lattice truss at five valuesof positive shear. Arrows indicate the loading direction. (b) The core is at thepeak stress level. Observable rupturing of truss members initiated by (c). (d)Only the compressed truss members continued to support the shear load.

Fig. 7. The normalized shear stiffness measurements vs. relative density. Exper-imental data represents the initial shear stiffness for both σ13 test orientationsand heat treatments. The error bars correspond to the 95% confidence level.

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nd Engineering A 472 (2008) 242–250

egative oriented shear directions and it can be seen in Fig. 8hat the normalized yield strength increases with relative den-ity. Note that the normalized coefficients shown in Fig. 8 areearly equivalent for both the annealed and aged lattice cores,ndicating a linear dependence upon σys of the parent alloy.

The normalized peak shear strength T = σpk/(σysρ̄) of thennealed and aged samples in the σ±13 orientation is plottedersus ρ̄ in Fig. 9. The experimental data for the normalizedeak strength of both the annealed and aged cores indicate aild dependence upon relative density for both the positive and

egative oriented shear samples. It can be seen in Fig. 9 that theormalized peak strengths increase with relative density and theate of increase in the annealed cores is nearly double that ofhe aged cores. This is indicative of the higher strain hardeningate of 6061 in the annealed condition. For example, the ratio ofTS/σys is an indication of the strain hardening capacity. Using

he data shown in Table 2, σTS/σys is 2.97 for the annealedondition and 1.14 for the aged condition.

. Micromechanical predictions

Deshpande and Fleck have developed analytical expressionsor the mechanical properties of tetrahedral lattice truss coresssuming elastic-ideally plastic struts [27]. Table 3 summarizesheir analytical expressions for the shear stiffness, Eqs. (2) and3), and strength, Eqs. (4) and (5). If the lattice is constructedrom slender trusses, they can collapse by elastic buckling. Inhis case, the shear strength is found by replacing σys in Eqs. (4)nd (5) with the elastic bifurcation stress, σcr, of the trusses, Eq.6). The factor k depends on the rotational stiffness of the nodes;or a pin-joint that can freely rotate k = 1 where k = 2 correspondso a built-in rigid joint. If the truss material has a non-zeroost-yield strain hardening rate, inelastic buckling defined byhanley–Engesser tangent modulus theory determines the latticetrength [47]. The peak compressive strength is then obtained byeplacing σys in Eqs. (4) and (5) with the inelastic bifurcationtress of a compressively loaded column. The inelastic bifur-ation stress, σcr, is given by Eq. (7) where, Et is the tangentodulus defined as the slope dσ/dε of the uniaxial stress versus

train curve of the parent material at a stress level, σcr [48].The shear stiffness in the σ±13 directions is predicted to be the

ame and its dependence upon ρ̄ is in very good agreement withhe experimental data (Fig. 7). The normalized shear strengthrediction, Eq. (5), is compared with the experimental data inig. 8 using the measured yield strength of the parent aluminum

o normalize the results. The experimental results approach theield strength predictions as the relative density increases foroth heat treated conditions and orientations. The discrepancyetween predicted and measured yield strengths at low relativeensity appears to be a manifestation of manufacturing defectsntroduced during fabrication.

The peak strength of lattice structures is determined by theirechanism of strut failure. This in turn depends on the truss

lenderness (cell geometry), strut material properties (i.e. yieldtrength, Young’s and tangent moduli) and the mode of load-ng. Peak shear strength predictions are also given in Table 3 foroth elastic and inelastic truss buckling. A comparison between

G.W. Kooistra et al. / Materials Science and Engineering A 472 (2008) 242–250 247

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ig. 8. Normalized shear yield strength vs. relative density for tetrahedral latticardened condition and for the σ−13 orientation in the (c) annealed and (d) aged

he measured and predicted normalized peak shear strength ishown in Fig. 9 for both test orientations and heat treatment con-itions. The peak shear strength prediction drawn on the figuresssumes inelastic buckling of the compressed truss members foroth node conditions (k = 1 and 2). Deshpande and Fleck havehown that the in-plane shear strength is periodic for the tetra-edral lattice core and it follows from symmetry conditions thathear strength in the σ±13 orientations are equivalent [27]. It

s apparent that the plastic buckling model predicts the higherelative density response of both the annealed and age hard-ned lattices reasonably well using a built-in node assumption.he lower relative density data is better approximated by a pin-

tcoa

able 3nalytical expressions for the in-plane shear stiffness and strength of the tetrahedral

echanical property Analytical

hear stiffness G = G13

ormalized shear stiffness Γ = G

Esρ̄hear strength (plastic yielding) σ = σ±13

ormalized shear strength (plastic yielding) T = σ

σysρ̄

hear strength (elastic buckling) σ = σ±13

hear strength (plastic buckling) σ = σ±13

ctures. Data are shown for the σ+13 orientation in the (a) annealed and (b) agedened condition.

ointed truss-facesheet connection condition consistent with lessnd constraint of slender trusses.

. Discussion

Numerous studies have addressed sandwich panel design forarious lattice truss sandwich structures [41,49–53]. Optimalesigns are ascertained by minimization of an objective func-

ion (normally weight) for panel bending, subject to multipleonstraints [41]. These constraints are normally defined by theperative failure mechanisms: facesheet yielding and bucklingnd truss member yielding and buckling. For most practical core

lattice [27]

expression

= 18 Es sin22ωρ̄ (2)

= 1

8sin22ω = 0.11, for ω = 54.7◦ (3)

= 14 σys sin2ωρ̄ (4)

= 1

4sin2ω = 0.24, for ω = 54.7◦ (5)

= 1

4σcr sin2ωρ̄, where σcr = k2π2Es

12

(t

l

)2

(6)

= 1

4σcr sin2ωρ̄, where σcr = k2π2Et

12

(t

l

)2

(7)

248 G.W. Kooistra et al. / Materials Science and Engineering A 472 (2008) 242–250

F e struch hard

tort

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tilattice data is shown for both negative and positive orientations.The two alloys have similar strain hardening characteristics andso we conclude that the tetrahedral lattice topology has an effi-ciency approaching that of a conventional hexagonal honeycomb

ig. 9. Normalized shear peak strength vs. relative density for tetrahedral latticardened condition and for the σ−13 orientation in the (c) annealed and (d) aged

opologies, optimal sandwich panel designs distribute 17–34%f the metal mass in the core, depending on topology with coreelative densities <10% and the remainder equally between theop and bottom facesheets [52].

The panels tested here are not optimized in this formal sense,ut it is still instructive to compare their response with hon-ycomb cores made from aluminum alloys of similar strength.he tetrahedral lattice is compared to an aluminum hexagonaloneycomb, and a (reentrant) flexible honeycomb both avail-ble from Hexcel Composites (Stamford, CT, USA) under therade names of HEXWEB® and FLEXCORE®. These honey-ombs are made from a 5052-H38 aluminum alloy for whichs = 69 GPa, σys = 255 MPa and σTS = 290 MPa [54]. The ratiof σTS/σys is an indication of the alloy strain hardening capac-ty. The ratio σTS/σy for 5052-H38 is very similar to that of the061-T6, 1.14 and 1.13, respectively. Both alloys also have sim-lar tensile failure strain values (14 and 17%, respectively) inheir high strength conditions. It is therefore possible to assesshe normalized lattice truss stiffness and strengths on a purelyopological basis.

Fig. 10 shows the stiffness of the tetrahedral lattice togetherith that of both the regular and flexible honeycomb. The shear

tiffness values in the figure correspond to the minimum shear

tiffness for both topologies. The tetrahedral lattice shear stiff-ess is nearly equivalent to the hexagonal honeycomb data ands ∼40% stiffer than that of flexible honeycombs of the sameore relative density. The tetrahedral lattices therefore appear to

Fc

tures. Data are shown for the σ+13 orientation in the (a) annealed and (b) agedened condition.

e attractive alternatives to conventional and especially flexibleoneycombs, for deflection limited applications.

Fig. 11 shows the normalized peak shear strengths for thewo honeycomb topologies loaded in the direction correspond-ng to the honeycombs minimum shear strength. The tetrahedral

ig. 10. The shear stiffness of the 6061-T6 tetrahedral lattices compared toommercially available 5052-H38 honeycomb cores.

G.W. Kooistra et al. / Materials Science and

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ig. 11. The normalized shear peak strength of the 6061-T6 tetrahedral latticeruss compared to commercially available 5052-H38 honeycomb.

nd appears significantly superior to flexible honeycomb struc-ures. Recalling the earlier study’s conclusion of comparableompressive strengths for the two topologies, we conclude thatetrahedral lattice structures appear to be promising alternativesor load supporting sandwich panel structures, especially whenhe structures posses significant curvature.

. Conclusions

Tetrahedral lattice cores have been made by folding hexago-nally perforated 6061 aluminum alloy sheets. A simple openair furnace brazing technique has then been used to metallur-gically bond the tetrahedral cores to 6951 solid facesheets toform sandwich panel structures.The shear stiffness and strength was experimentally measuredand their behavior was adequately captured by Deshpandeand Fleck’s analytical expressions for modulus and strengthof tetrahedral lattice truss structures.The structural performance of the 6061 tetrahedral latticeslie within in the upper and lower bounds of conventionalhexagonal honeycomb shear stiffness and are competitivewith honeycomb topologies when loaded in the minimumshear strength directions.The tetrahedral lattice core is highly flexible prior to bondingto facesheets and it is more than 40% stiffer and stronger thanequivalent relative density flexible honeycombs used for thecores of curved sandwich panels.The tetrahedral lattice structure offers many ancillary benefitsto traditional closed-celled honeycombs all at an equivalentspecific stiffness and strength while possessing the formabil-ity of flexible honeycomb topologies.

cknowledgements

This work was supported by the Office of Naval ResearchONR), monitored by Drs. Steve Fishman and David Shifler

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Engineering A 472 (2008) 242–250 249

nder grant number N00014-01-1-1051. The authors are espe-ially grateful to Vikram Deshpande (Cambridge University) forany helpful discussions.

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