Approximation of anisotropic elasticity tensors at the reference state with polyconvex energies

For simulations of boundary value problems using anisotropic hyperelastic constitutive equations at moderate strains anisotropic polyconvex energies can preferably be used because the existence of minimizers is then automatically guaranteed. For this reason, we investigate the adaptability of anisotropic polyconvex energy functions for the phenomenological description of real anisotropic material responses. Here we focus on the fitting of the fourth-order tangent moduli near the reference state to some experimental data of anisotropic materials. We use anisotropic energies which can be generated for arbitrary anisotropy classes and automatically satisfy the polyconvexity condition. In this paper we consider orthotropic and monoclinic materials.