On a class of nonlinear isotropic thermo-elastic body that is non-Green elastic: Applications to large elastic deformations

Abstract

Summary A new class of constitutive equation is proposed for isotropic thermoelastic solids, wherein the Hencky strain tensor is assumed to be a function of the Cauchy stress tensor, via a Gibbs potential. The solid is assumed to be incompressible in the referential state, but the volume can change due to differences in the temperature relative to a reference temperature. The change in volume only depends on temperature. Some restrictions are found for the Gibbs potential, resulting in a constitutive equation for isotropic solids, wherein the volume depends on temperature. Using the resulting constitutive equation, some boundary value problems are studied, considering some relatively simple distributions for the temperature, deformations and stresses.