THERMODYNAMICALLY CONSISTENT SET OF EXPLICIT CONSTITUTIVE STATE EQUATIONS FOR INELASTIC SOLIDS

Abstract

This study applies the theory of continuum thermodynamics with internal state variables to determine the nature of and the restrictions on the constitutive response functions of inelastic solids. An explicit expression for the Helmholtz free energy functional is then proposed leading to explicit expressions for stress and entropy functionals in terms of thermodynamic state variables. The temperature-dependent thermoinelastic material properties involved are determined by a novel application of the results of thermodynamics, materials science and mechanics experiments, and mathematical analysis. The state equations in conjunction with the heat conduction equation and the evolution laws for the internal state variables give a complete formulation of the constitutive relations. The nonlinear material model so developed is applicable over a wide range of temperatures and takes into consideration thermomechanical coupling in addition to the coupling of thermoelastic and thermoinelastic variables. It also explicitly gives the dissipative part of the stress thereby eliminating the need for a separate dissipation potential. It is suitable for thermomechanical studies under nonisothermal and nonadiabatic situations.