A homogenization result in finite plasticity

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