Calculus of Variations and Geometric Measure Theory

E. Davoli - C. Gavioli - V. Pagliari

A homogenization result in finite plasticity and its application to high-contrast media

created by davoli on 19 Apr 2022

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Submitted Paper

Inserted: 19 apr 2022
Last Updated: 19 apr 2022

Year: 2022

Abstract:

We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure, we firstly establish the Γ-convergence of the energies in the limiting of vanishing periodicity. Then, in the second part of the paper, we use the result to derive a macroscopic description for an elastoplastic medium with high-contrast microstructure. Specifically, we consider a composite obtained by filling the voids of a periodically perforated stiff matrix by soft inclusions. Again, we study the Γ-convergence of the related energy functionals as the periodicity tends to zero. The main challenge is posed by the lack of coercivity brought about by the degeneracy of the material properties in the soft part. We prove that the Γ-limit, which we compute with respect to a suitable notion of convergence, is the sum of the contributions resulting from each of the two components separately.

Keywords: Homogenization, finite plasticity, high-contrast


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