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 sta te variables, the two laws of thermodynamics are used to determine the thermodynamic potentials as the internal energy and the entropy and t hen to construct a relative energy function for the quasilinear temper ature 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 identi ty/inequality to find energetic bounds in terms of the input data for continuous solutions of initial-boundary value problems. The same ener gy 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 presen ted in the case when the constitutive equations are given such that th e instantaneous elastic response in stress, internal energy and entrop y exists. Explicit forms of the thermodynamic potentials for linear th ermo-viscoelasticity and a Sokolovskii type thermoviscoplastic model a re given. (C) 1998 Elsevier Science Ltd. All rights reserved.