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A mathematical model for an elastoplastic continuum subject to large strainsis presented. The inelastic response is modeled within the frame ofrate-dependent gradient plasticity for nonsimple materials. Heat diffusesthrough the continuum by the Fourier law in the actual deformed configuration.Inertia makes the nonlinear problem hyperbolic. The modelling assumption ofsmall elastic Green-Lagrange strains is combined in a thermodynamicallyconsistent way with the possibly large displacements and large plastic strain.The model is amenable to a rigorous mathematical analysis. The existence ofsuitably defined weak solutions and a convergence result for Galerkinapproximations is proved.

Finite thermoelastoplasticity and creep under small elastic strains