Polyconvex Energies for Trigonal, Tetragonal and Cubic Symmetry Groups

Abstract

In large strain elasticity the existence of minimizers is guaranteed if the variational functional to be minimized is sequentially weakly lower semicontinuous (s.w.l.s.) and coercive. Therefore, for the description of hyperelastic materials polyconvex functions which are always s.w.l.s. should be preferably used. A variety of isotropic and anisotropic polyconvex energies, in particular for the triclinic, monoclinic, rhombic and transversely isotropic symmetry groups, already exist. In this contribution we propose a new approach for the description of trigonal, tetragonal and cubic hyperelastic materials in the framework of polyconvexity. The anisotropy of the material is described by invariants in terms of the right Cauchy’Green tensor and a specific fourth-order structural tensor. In order to show the adaptability of the introduced polyconvex energies for the approximation of real anisotropic material behavior we focus on the fitting of a trigonal fourth-order tangent moduli near the reference state to experimental data.