Commutability of homogenization and linearization at identity in finite elasticity and applications |
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Authors: | Antoine Gloria Stefan Neukamm |
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Institution: | aProject-team SIMPAF & Laboratoire Paul Painlevé UMR 8524, INRIA Lille – Nord Europe & Université Lille 1, Villeneuve d?Ascq, France;bMax Planck Institute for Mathematics in the Sciences, Inselstr. 22–26, D-04103 Leipzig, Germany |
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Abstract: | 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 Γ-convergence commutation diagram for linearization and homogenization to the stochastic setting under standard growth conditions. As a second application, we prove that the Γ-closure is local at identity for this class of energy densities. |
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Keywords: | MSC: 35B27 49J45 74E30 74Q05 74Q20 |
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