The set of all equilibrium states of a two-phase thermoelastic medium. Part 1: existence of equilibrium states of a two-phase thermoelastic medium

Abstract

This article is the first 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 two-phase 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 strestemperature 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 and the stress-temperature tensors, the solvability of the problem of the equilibrium of a two-phase thermoelastic medium is proved and the description of the set of all equilibrium states of a two-phase thermoelastic medium is given.

Keywords:

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