Calculus of Variations and Geometric Measure Theory

E. Davoli - C. Gavioli - V. Pagliari

A homogenization result in finite plasticity

created by davoli on 13 Dec 2022
modified by gavioli on 19 Mar 2024


Accepted Paper

Inserted: 13 dec 2022
Last Updated: 19 mar 2024

Journal: Calc. Var. PDEs
Volume: 63
Pages: 72
Year: 2024
Doi: 10.1007/s00526-024-02673-0

ArXiv: 2204.09084 PDF


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 establish the Γ-convergence of the energies in the limiting of vanishing periodicity. The constraint that plastic deformations belong to SL(3) poses the biggest hurdle to the analysis, and we address it by regarding SL(3) as a Finsler manifold.

Keywords: Homogenization, $\Gamma$-convergence, Finsler manifold, finite-strain elastoplasticity