Nonlinear Constitutive Relations of Thermoelasticity for Anisotropic Bodies

Abstract

One of the ways to describe the reaction of an anisotropic elastic body to external force and thermal influences is to construct functional dependencies of the measure of finite deformations on the stress tensor and temperature. To find such dependencies, the inverse thermomechanical problem is formulated. The solution of the thermomechanical problem is based on the use as hypotheses of generalizations of A.A. Ilyushin particular isotropy postulate, formulated for finite deformations of anisotropic bodies. Nonlinear dependencies of the strain tensor on the stress tensor and temperature are obtained using the Gibbs thermodynamic potential.