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Journal Articles Annales de l'Institut Henri Poincaré C, Analyse non linéaire Year : 2011

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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Dates and versions

inria-00540615 , version 1 (28-11-2010)

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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, Analyse non linéaire, 2011, 28, pp.941-964. ⟨10.1016/j.anihpc.2011.07.002⟩. ⟨inria-00540615⟩
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