Construction of anisotropic polyconvex energies and applications to thin shells

In computer simulations where constitutive equations are considered anisotropic polyconvex energies can preferably be used because the existence of minimizers is then automatically guaranteed. In this work we investigate the capability to simulate anisotropy effects of anisotropic thin shells using polyconvex anisotropic energies. The construction of the considered polyconvex transversely isotropic energy is based on specific structural tensors. The iterative enforcement of the zero normal stress condition at the integration points allows the consideration of arbitrary three-dimensional constitutive equations. As a representative example we compare results for isotropic and anisotropic plates.