A transversely isotropic viscohyperelastic material: Application to the modeling of biological soft connective tissues

Abstract

A general transversely isotropic viscohyperelastic constitutive law including strain rate effects was proposed. It is based on a definition of a general Helmholtz free energy function which depends explicitly on the right Cauchy–Green deformation tensor, its material time derivative and a structural tensor characterizing the preferred direction from which anisotropy arises. The elastic and viscous potentials that defined the free energy function were assumed to be decoupled, thus facilitating the identification process. This law was valid for arbitrary kinematics and aimed at modeling the mechanical behavior of biological soft tissues at high strain rates and at the finite strain regime. This is of high relevance for dynamic analyses of human occupants in car crash simulations (finite element analyses) and for situations where dynamic loads are significant (sport injury, etc). Explicit expression of the stress, elasticity and viscosity tensors were established. As an application of the constitutive law, the general expressions of the stress tensors were particularized for a specific Helmholtz free energy function describing the mechanical characteristics of the human anterior cruciate ligament. The constitutive model was shown to capture the strain rate effects and other essential characteristics of ligaments such as finite strain, anisotropy and nearly incompressibility. The model was also tested for various multi-axial loading situations.