  A mathematical model for an elastoplastic continuum subject to large strains
is presented. The inelastic response is modeled within the frame of
rate-dependent gradient plasticity for nonsimple materials. Heat diffuses
through the continuum by the Fourier law in the actual deformed configuration.
Inertia makes the nonlinear problem hyperbolic. The modelling assumption of
small elastic Green-Lagrange strains is combined in a thermodynamically
consistent way with the possibly large displacements and large plastic strain.
The model is amenable to a rigorous mathematical analysis. The existence of
suitably defined weak solutions and a convergence result for Galerkin
approximations is proved.
