Energy estimates in rate-type thermo-viscoplasticity

Based on the knowledge on the stress, strain and temperature relation, the dependence of the specific heat and of the latent heat on the state variables, the two laws of thermodynamics are used to determine the thermodynamic potentials as the internal energy and the entropy and then to construct a relative energy function for the quasilinear temperature dependent rate-type constitutive equations. The relative energy is a positive valued function of strain, temperature and stress in all cases of practical interest. Next, one uses the derived energy identity/inequality to find energetic bounds in terms of the input data for continuous solutions of initial-boundary value problems. The same energy identity is used to obtain precise estimates, in terms of the same input data, for the deviation of the process from the equilibrium. An explicit procedure to determine the thermodynamic potentials is presented in the case when the constitutive equations are given such that the instantaneous elastic response in stress, internal energy and entropy exists. Explicit forms of the thermodynamic potentials for linear thermo-viscoelasticity and a Sokolovskii type thermoviscoplastic model are given. (C) 1998 Elsevier Science Ltd. All rights reserved.