Integrity basis of polyconvex invariants for modeling hyperelastic orthotropic materials - Application to the mechanical response of passive ventricular myocardium

The present paper proposes a new Strain Energy Function (SEF) for modeling incompressible orthotropic hyperelastic materials with a specific application to the mechanical response of passive ventricular myocardium. In order to build our SEF, we have followed a classical strategy based on exponential functions, but we have chosen to work with polyconvex invariants instead of the standard ones. Actually, in the context of hyperelastic problems, the polyconvexity of the strain energy density is considered as a prerequisite for ensuring the existence of solutions. By selecting a set of polyconvex invariants, we demonstrate that our model can predict the experimental data with 6 different shear modes applied to passive ventricular myocardium.