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

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.
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Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2011, 28, pp.941-964. 〈10.1016/j.anihpc.2011.07.002〉
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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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