The set of all equilibrium states of a two-phase thermoelastic medium. Part 2: Dependence of the set of all equilibrium states of a two-phase thermoelastic medium on the temperature

Abstract

This article is the second part of the work devoted to the study of the set of all equilibrium states of a two-phase thermoelastic medium. The equilibrium state of a twophase elastic medium is understood as an ordered pair: a displacement field and a spatial phase distribution which provide the free energy functional with a global minimum. For thermoelastic media, the free energy densities are obtained by adding to the strain energy densities the terms associated with the temperature stresses of each phase and the terms associated with the energies of each phase in the unstressed state at zero stres-temperature tensors. Under zero Dirichlet boundary conditions on the displacement field and certain restrictions on the elasticity tensors, the strain tensors providing each phase with the unstressed state at the initial temperature, the stres-temperature tensors and the terms in the definition of the free energy densities associated with the energies of each phase in the unstressed state at zero stres-temperature tensors the dependence of the set of all equilibrium states of a two-phase thermoelastic medium on the temperature is found and studied.

Keywords:

two-phase thermoelastic medium, free energy functional, free energy density, spatial phase distribution, equilibrium state