Finite anisotropic elasticity and material frame indifference from a nonequilibrium thermodynamics perspective

A closed set of Eulerian evolution equations for nonisothermal finite isotropic and anisotropic elastic behavior is derived using nonequilibrium thermodynamics. In particular, it is shown that to describe the state of elastic deformation, the deformation gradient F is preferred as internal variable to the more well-known left and right Cauchy-Green strain tensors. With the energy and entropy functions being frame invariant, the stress tensor expression as obtained in terms of F satisfies the principle of material frame indifference. As an alternative to the F-formulation, it is also shown how elasticity can be described in terms of the mass density and the isochoric deformation gradient, F˜=F/det⁡F3, instead.