On the computation of configurational forces in anisotropic hyperelastic solids

In the field of configurational mechanics we study energetic changes associated to variations of material configurations. The central part in this notion is the energy momentum tensor, also known as the Eshelby stress tensor, which enters the configurational force balance. The mechanics of material forces has been successfully applied to a variety of important fields in applied mechanics such as e.g. the evolution of interfaces, growth in biomechanical systems, the kinetics of dislocations, fracture mechanics, morphology/structure optimization in heterogeneous microstructures. In most contributions configurational forces are computed for isotropic bodies; in this presentation we consider the influence of anisotropy. As a specific model problem we consider a single-edged-tension specimen, where we analyze the sensitivity of the configurational forces in amplitude and orientation with respect to changing main axes of anisotropy of a hyperelastic material. These configurational forces can be interpreted as driving forces on the crack tips of the considered boundary value problem, which are directly related to the classical J -integral in fracture mechanics. In order to guarantee the existence of minimizers we use an anisotropic polyconvex energy. Here, we focus on a transversely isotropic constitutive law formulated in the framework of invariant theory