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