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.

本文提出了一种新的应变能函数（SEF），用于建模不可压缩的正交各向异性超弹性材料，特别适用于被动心室心肌的机械反应。为了构建SEF，我们遵循了基于指数函数的经典策略，但是我们选择使用多凸不变量而不是标准不变量。实际上，在超弹性问题的背景下，应变能密度的多凸性被认为是确保解存在的前提。通过选择一组多凸不变量，我们证明了我们的模型可以预测应用于被动心室心肌的6种不同剪切模式的实验数据。