Material-symmetries congruency in transversely isotropic and orthotropic hyperelastic materials

In this work we present the material-symmetries congruency property for anisotropic hyperelastic materials. A transversely isotropic or orthotropic material model holding this property guarantees the recovery of the isotropic behavior when, for example, the volume of reinforcement in a composite material vanishes. A material presenting material-symmetries congruency must show it not only from an analytical, theoretical point of view, but also from a numerical, practical point of view. The former may be obtained from construction of the stored energy function, whereas the latter must be obtained guaranteeing that the parameter-fitting procedure yields material parameters which combined with the specific model results in an isotropic behavior prediction for isotropic materials. We show that some anisotropic models do not present either analytical or numerical material-symmetries congruency.