Two different approaches to model evolving directional properties at finite deformations

Two different approaches to modeling evolving anisotropic material behavior are investigated. The first approach models the evolution of the directionally dependent properties of the material in terms of evolution laws for the director vectors. In the second approach the evolution law for the plastic velocity gradient is enhanced by additional terms. It is shown that both approaches lead to an evolution of the substructure that guides the directionally dependent properties of the material. The two approaches are analyzed within a thermodynamic setting and the restrictions imposed by the second law of thermodynamics are investigated. The two approaches are also compared from a kinematic point of view and equivalence between the two approaches is shown for some specific conditions. To further compare the approaches in the case in which equivalence cannot be found, two different evolution laws are considered, one for the substructure and the other for the plastic velocity gradient. These are compared for a loading that corresponds to a plane strain volume preserving deformation as well as simple shear. Here the Kirchhoff stress and the evolution of the director vectors are studied during the deformation process.