A homogenization result in finite plasticity

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