On the use of evolving structure tensors to model initial and induced elastic and inelastic anisotropy at finite deformation

Abstract

The purpose of this work is the formulation and application of an approach to the phenomenological modeling of a class of materials which may in general exhibit anisotropic elastic and inelastic behaviour at large deformation. This is done in the framework of a thermodynamic, intemal-variable-based formulation for such behaviour as based on two basic assumptions: (i), the modeling of the local inelastic deformation in the material as a material isomorphism, and (ii), the modeling of the internal variables as structure tensors. The first of these assumptions follows from the idea that the local inelastic deformation does not influence the form of the dependence of the constitutive relations on the other independent constitutive variables. As shown in earlier work, one consequence of this assumption is the multiplicative decomposition of the deformation gradient into elastic and inelastic parts. And from a thermodynamic point of view, it is consistent with the idea that only a part of the local deformation results in energy storage in the material. Assumption (ii) leads among other things to concrete forms for the constitutive relations and the reduction of the flow rule to an evolution relation for the plastic right Cauchy-Green deformation or its inverse for general anisotropic behaviour. Finally, application of the general approach to the special cases of (1), non-linear kinematic and isotropic hardening in metals, and (2), anisotropic polymer membranes, is briefly discussed and demonstrated.