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arXiv · 1011.3783

On the commutability of homogenization and linearization in finite elasticity

Stefan Müller·Stefan Neukamm
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Abstract

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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Stefan Müller, Stefan Neukamm. 2011-05-16. On the commutability of homogenization and linearization in finite elasticity. https://doi.org/10.1007/s00205-011-0438-7

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