Application of the concept of evolving structure tensors to the modeling of initial and induced anisotropy at large deformation

In this work, a thermodynamic approach to the modeling and simulation of induced elastic and inelastic material behaviour in the phenomenological realm as based on the concept of evolving structure tensors is discussed. From the constitutive point of view, these quantities determine the material symmetry properties. In addition, the stress and other dependent constitutive fields are isotropic functions of these by definition. The evolution of these during loading then results in an evolution of the anisotropy of the material. From an algorithmic point of view, the current approach leads to constitutive models which are quite amenable to numerical implementation. To demonstrate the applicability of the resulting constitutive formulation, we apply it to the cases of (i) metal plasticity with combined hardening involving both deformation- and permanently induced anisotropy relevant to the modeling of processes such as metal forming, and to (ii) deformation-induced anisotropy in an initially orthotropic pneumatic membrane consisting of a rubber matrix and nylon fibres.