Constitutive Model for Anterior Leaflet of Heart with Physical Invariants

Abstract

Much research has been done in determining constitutive models for Nonlinear Transversely Isotropic Solids. The strain energy functions with different types of invariants were developed in the past to serve some purposes. In isotropic elasticity, phenomenological strain energy functions with principal stretches have certain attractive features from both the mathematical and physical viewpoints. These forms of strain energy have been widely and successfully used in predicting elastic deformations. In this paper, we extend these successful principal-stretches-isotropic models to characterise transversely isotropic solids based on previous work. We introduce five invariants that have immediate physical interpretation. Three of the invariants are the principal extension ratios and the other two are the cosines of the angles between the principal directions of the right stretch tensor and the material preferred direction. This model has an experimental advantage and the theory is compared well with experimental data.