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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on November 13, 2006
The Quarterly Journal of Mechanics and Applied Mathematics 2006 59(4):615-630; doi:10.1093/qjmam/hbl017
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Q. Jl Mech. Appl. Math, Vol. 59. No. 4 © The author 2006. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Instabilities in elastomers and in soft tissues

A Goriely{dagger}

( Program in Applied Mathematics and Department of Mathematics, University of Arizona, Building 89, Tucson, AZ 85721, USA )

M Destrade{ddagger}

( Laboratoire de Modélisation en Mécanique, CNRS (UMR7607), Université Pierre et Marie Curie, Case 162, 4 Place Jussieu, 75252 Paris Cedex 05, France )

M Ben Amar§

( Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France )

{dagger} goriely{at}math.arizona.edu

{ddagger} Corresponding author: destrade{at}lmm.jussieu.fr

§ benamar{at}lps.ens.fr


  Abstract

Biological soft tissues exhibit elastic properties that can be dramatically different from rubber-type materials (elastomers). To gain a better understanding of the role of constitutive relationships in determining material responses under loads we compare three different types of instabilities (two in compression, one in extension) in hyperelasticity for various forms of strain-energy functions typically used for elastomers and for soft tissues. Surprisingly, we find that the strain-hardening property of soft tissues does not always stabilize the material. In particular we show that the stability analyses for a compressed half-space and for a compressed spherical thick shell can lead to opposite conclusions: a soft tissue material is more stable than an elastomer in the former case and less stable in the latter case.


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