Calculus of Variations and Geometric Measure Theory

E. Davoli - C. Gavioli - V. Pagliari

Homogenization of high-contrast media in finite-strain elastoplasticity

created by pagliari on 30 Dec 2022


Submitted Paper

Inserted: 30 dec 2022
Last Updated: 30 dec 2022

Year: 2022


This work is devoted to the analysis of the interplay between internal variables and high-contrast microstructure in inelastic solids. As a concrete case-study, by means of variational techniques, we derive a macroscopic description for an elastoplastic medium. Specifically, we consider a composite obtained by filling the voids of a periodically perforated stiff matrix by soft inclusions. We study the $Gamma$-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 $\Gamma$-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. Eventually, convergence of the energy minimizing configurations is obtained.

Keywords: Homogenization, $\Gamma$-convergence, Two-scale convergence, high-contrast, finite-strain elastoplasticity