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We consider a thermodynamically consistent model for thermoviscoplasticity.For the related PDE system, coupling the heat equation for the absolutetemperature, the momentum balance with viscosity and inertia for thedisplacement variable, and the flow rule for the plastic strain, we propose twoweak solvability concepts, 'entropic' and 'weak energy' solutions, where thehighly nonlinear heat equation is suitably formulated. Accordingly, we provetwo existence results by passing to the limit in a carefully devised timediscretization scheme.  Furthermore, we study the asymptotic behavior of weak energy solutions as therate of the external data becomes slower and slower, which amounts to takingthe vanishing-viscosity and inertia limit of the system. We prove theirconvergence to a global energetic solution to the Prandtl-Reuss model forperfect plasticity, whose evolution is `energetically' coupled to that of the(spatially constant) limiting temperature.

From visco to perfect plasticity in thermoviscoelastic materials