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MiS Preprint
73/2010

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

Antoine Gloria and Stefan Neukamm

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.

Received:
Nov 30, 2010
Published:
Dec 20, 2010
MSC Codes:
35B27, 49J45, 74E30, 74Q05, 74Q20
Keywords:
homogenization, nonlinear elasticity, linearization, Gamma-closure

Related publications

inJournal
2011 Repository Open Access
Antoine Gloria and Stefan Neukamm

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

In: Annales de l'Institut Henri Poincaré / C, 28 (2011) 6, pp. 941-964