# Commutability of homogenization and linearization at identity in finite elasticity and applications

1 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
Abstract : In this note we prove under some general assumptions on elastic energy densities (namely, frame indifference, minimality at identity, non-degeneracy and existence of a quadratic expansion at identity) that homogenization and linearization commute at identity. This generalizes a recent result by S.~Müller and the second author by dropping their assumption of periodicity. As a first application, we extend their $\Gamma$-convergence commutation diagram for linearization and homogenization to the stochastic setting under standard growth conditions. As a second application, we prove that the $\Gamma$-closure is local at identity for this class of energy densities.
Type de document :
Article dans une revue
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2011, 28, pp.941-964. 〈10.1016/j.anihpc.2011.07.002〉

Littérature citée [13 références]

https://hal.inria.fr/inria-00540615
Contributeur : Antoine Gloria <>
Soumis le : dimanche 28 novembre 2010 - 17:28:26
Dernière modification le : mercredi 25 avril 2018 - 14:23:16
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Antoine Gloria, Stefan Neukamm. Commutability of homogenization and linearization at identity in finite elasticity and applications. Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2011, 28, pp.941-964. 〈10.1016/j.anihpc.2011.07.002〉. 〈inria-00540615〉

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