Capturing anisotropic constitutive models with WYPiWYG hyperelasticity; and on consistency with the infinitesimal theory at all deformation levels

The elastic nonlinear behavior of fiber-reinforced materials and soft biological tissues is analyzed using anisotropic hyperelastic models. Frequently, these models are not compatible with the corresponding infinitesimal theory, but some of them may be modified to accommodate that theory in the limit. WYPiWYG hyperelasticity is compatible with the infinitesimal theory at all deformation levels and capable of capturing exactly a complete set of experimental data, which reproduces all deformation modes at every strain level, under homogeneous deformations. In this work we study the relevance of recovering the infinitesimal theory at every deformed configuration and also the performance of the WYPiWYG method in predicting the behavior of anisotropic materials at large strains under nonhomogeneous deformations.