On the commutability of homogenization and linearization in finite elasticity

Details On the commutability of homogenization and linearization in finite elasticity On the commutability of homogenization and linearization in finite elasticity

2010-11-16

arxiv.org/abs/1011.3783v3

Mathematics

Analysis of PDEs

Scientific paper

We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor expansion at identity, we prove that the Gamma-limits associated to homogenization and linearization commute. Moreover, we show that the homogenized energy density, which is determined by a multi-cell homogenization formula, has a quadratic Taylor expansion with a quadratic term that is given by the homogenization of the quadratic term associated to the linearization of the initial energy density.

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