A generalized orthotropic hyperelastic material model with application to incompressible shells

In the present paper a new orthotropic hyperelastic constitutive model is proposed which can be applied to the numerical simulation of a wide range of anisotropic materials and particularly biological soft tissues. The model represents a non-linear extension of the orthotropic St. Venant{Kirchho material and is described in each principal material direction by an arbitrary isotropic tensor function coupled with the corresponding structural tensor. In the special case of isotropy this constitutive formulation reduces to the Valanis{Landel hypothesis and may therefore be considered as its generalization to the case of orthotropy. Constitutive relations and tangent moduli of the model are expressed in terms of eigenvalue bases of the right Cauchy{ Green tensor C and obtained for the case of distinct and coinciding eigenvalues as well. For the analysis of shells the model is then coupled with a six ( ve in incompressible case) parametric shell kinematics able to deal with large strains as well as nite rotations. The application of the developed nite shell element is nally illustrated by a number of numerical examples