An Anisotropic Material Model for Finite Rubber Viscoelasticity

In this article a formulation of an anisotropic finite linear viscoelasticity model is proposed. In particular, transverse isotropy and orthotropy is considered. The aim of this work is to establish a material model, which allows the description of an anisotropic material response in the framework of the finite deformation theory. First of all, the fundamentals of finite hyperelasticity are discussed. In the next step, we consider a finite linear viscoelastic formulation which is then extended to the theory of anisotropy. After giving an introduction to the coordinate free representation of anisotropic material behaviour using isotropic tensor functions in terms of structural tensors, we derive the constitutive equations for the orthotropic linear viscoelasticity model. This model is implemented into the nonlinear finite element code LS-DYNA. Both, an explicit and an implicit implementation is carried out. To evaluate the performance of the model, representative numerical examples are discussed in detail.