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Abstract <p>In this paper, the second part of studying the set of all equilibrium states of a two-phase thermoelastic medium has been presented. An 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 the terms associated with the thermal stresses of each phase and the terms associated with the energies of each phase in the unstressed state at zero stress-temperature tensors to the strain energy densities. The temperature dependence of the set of all equilibrium states of a two-phase thermoelastic medium has been found and studied 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, the stress-temperature tensors, and terms in the definition of the free energy densities associated with the energies of each phase in the stress-free state at zero stress-temperature tensors.</p>

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The Temperature Dependence of the Set of All Equilibrium States of a Two-Phase Thermoelastic Medium

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • E. A. Efimov

摘要

Abstract

In this paper, the second part of studying the set of all equilibrium states of a two-phase thermoelastic medium has been presented. An 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 the terms associated with the thermal stresses of each phase and the terms associated with the energies of each phase in the unstressed state at zero stress-temperature tensors to the strain energy densities. The temperature dependence of the set of all equilibrium states of a two-phase thermoelastic medium has been found and studied 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, the stress-temperature tensors, and terms in the definition of the free energy densities associated with the energies of each phase in the stress-free state at zero stress-temperature tensors.