*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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