On the Existence and the Set of All Equilibrium States of a Two-Phase Thermoelastic Medium

This work is the first part of a study focused on the set of all equilibrium states of a two-phase thermoelastic medium. By the equilibrium state of a two-phase elastic medium an ordered pair is meant: 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 stress-free state at zero stress-temperature tensors. The solvability of the problem of two-phase thermoelastic medium equilibrium is proved under zero Dirichlet boundary conditions on the displacement field and certain restrictions on the elasticity tensors, the strain tensors providing each phase with the stress-free state at the initial temperature and the stress-temperature tensors, and the set of all equilibrium states of a two-phase thermoelastic medium is described.