# Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity

3 SIMPAF - SImulations and Modeling for PArticles and Fluids
Inria Lille - Nord Europe, LPP - Laboratoire Paul Painlevé - UMR 8524
Abstract : This article is devoted to the study of the asymptotic behavior of a class of energies defined on stochastic lattices. Under polynomial growth assumptions, we prove that the energy functionals $F_\e$ stored in the deformation of an $\e$-scaling of a stochastic lattice $\Gamma$-converge to a continuous energy functional when $\e$ goes to zero. In particular, the limiting energy functional is of integral type, and deterministic if the lattice is ergodic. We also generalize to systems and nonlinear settings well-known results on stochastic homogenization of discrete elliptic equations. As an application of the main result, we prove the convergence of a discrete model for rubber towards the nonlinear theory of continuum mechanics. We finally address some mechanical properties of the limiting models, such as frame-invariance, isotropy and natural states.
Type de document :
Article dans une revue
Archive for Rational Mechanics and Analysis, Springer Verlag, 2011, 200, pp.881-943. 〈10.1007/s00205-010-0378-7〉

Littérature citée [44 références]

https://hal.inria.fr/inria-00437765
Contributeur : Antoine Gloria <>
Soumis le : mardi 1 décembre 2009 - 14:06:04
Dernière modification le : mardi 3 juillet 2018 - 11:38:03
Document(s) archivé(s) le : jeudi 17 juin 2010 - 20:23:51

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Roberto Alicandro, Marco Cicalese, Antoine Gloria. Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity. Archive for Rational Mechanics and Analysis, Springer Verlag, 2011, 200, pp.881-943. 〈10.1007/s00205-010-0378-7〉. 〈inria-00437765〉

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