On Anisotropy, Objectivity and Invariancy in finite thermo–mechanical deformations

In elastic–plastic finite deformation problems constitutive relations are commonly formulated in terms the Cauchy stress as a function of the elastic finger tensor and an objective rate of the Cauchy stress as a function of the rate of deformation tensor. For isotropic materials models this is rather straight forward, but for anisotropic material models, including elastic anisotropy as well as plastic anisotropy, this may lead to confusing formulations. It will be shown that it is more convenient to define the constitutive relations in terms of invariant tensors referred to the deformed metric. An alternative decomposition of the deformation tensor is introduced that can easily be linked to the additive decomposition of the velocity gradient into a spin tensor and a rate of deformation tensor. Constraints for constitutive equations are formulated based on thermodynamics.