May 21, 2024Open Access

Upper bounds for the homogenization problem in nonlinear elasticity: the incompressible case

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Abstract

We consider periodic homogenization of hyperelastic models incorporating incompressible behavior via the constraint (u) =1. We show that the 'usual' homogenized integral functional W ₇₎₌ (u) \, dx, where W ₇₎₌ is the standard multicell-formula of non-convex homogenization restricted to volume preserving deformations, yields an upper bound for the -limit as the scale of periodicity tends to zero.

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Ruf et al. (Tue,) studied this question.

synapsesocial.com/papers/68e69359b6db643587619e35 https://doi.org/https://doi.org/10.48550/arxiv.2405.12877

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