5.5 Isotropic Thermoelastic Materials

An isotropic material is defined as one that has a reference configuration R ₀ with respect to which material properties are the same in all directions. Said differently, rotations of the reference configuration R ₀ cannot be detected by subsequent thermomechanical experiments. To make this statement more precise, we work in terms of the heat flux q measured per unit area in the present configuration; Eq. (4.87) gives the relation between q and Q. Equations (5.8) ₂ and (4.87) imply that, for a thermoelastic material, the present value of q at the current location of the material point X depends upon F ( X, t ), ?( X, t), and g ( X, t) since

That is,

An advantage of working in terms of q and g is that they are measured in the present configuration of the body.

A thermomechanical experiment for a thermoelastic material involves the application of the deformation gradient F, the temperature change ( ? ? ? ₀ ), and the temperature gradient corresponding to g in the reference configuration, and measuring present values of the Helmholtz free energy ( F, ?) and the heat flux q ( F, ?, g ). Thus for a thermoelastic material isotropic in the reference configuration R ₀, the application of the deformation gradient F, the temperature...