On the comparison of two strategies to formulate orthotropic hyperelasticity

The main goal of this work is to clarify the relation between two strategie s to formulate constitutive equations for orthotropic materials at large st rains. On the one hand, the classical approach is based on the incorporatio n of structural tensors into the free energy function via an enriched set o f invariants. On the other hand, a fictitious isotropic configuration is in troduced which renders an anisotropic, undeformed reference configuration v ia an appropriate linear tangent map. This formulation results in a reduced (with respect to the more general setting based on structural tensors) but nevertheless physically motivated set of invariants which are related to t he invariants defined by structural tensors. As a main conceptual advantage standard isotropic constitutive equations can be applied and moreover, due to the reduced set of physically motivated invariants, the numerical treat ment within a finite element setting becomes manageable.