Predicting Articular Cartilage Behavior with a Non-Linear Microstructural Model

Abstract

We report here on a non-linear poroelastic model for the mechanical response of collagenous soft tissues such as articular cartilage. The tissue consists of a porous, fibril-reinforced, hyperelastic solid, saturated with an incompressible fluid, and Darcy's law governs solid-fluid interaction. The solid matrix is characterized by the isotropic hyperfoam strain energy function and its permeability is made to depend on local strain. The fibrils are non-linear, provide tensile stiffness only, exhibit viscoelasticity and have arbitrary, three-dimensional, statistical distributions. The stress tensor in the fibril network is calculated from the constitutive law for a single fibril with the aid of the fibril distribution functions. With a specific viscoelastic fibril constitutive relationship and a three-layered cartilage construction, the model is shown to pre- dict well strain-dependent and time-dependent behavior in unconfined compression and tension and in unconfined com- pression and indentation, using identical sets of material parameters.