On the numerical simulation of the mechanical behaviour of articular cartilage

In this paper, a fibre-reinforced porohyperelastic model is extensively presented and used for the simulation of soft hydrated tissues, like cartilage. The derivation of the classical governing equations for biphasic tissues is obtained from a complete and robust description for multiphasic systems. An Augmented Lagrangian formulation has been used to enforce the incompressibility condition in the whole tissue. Porohyperelasticity has been included in order to simulate the biphasic nature of the tissue associated to a porous solid matrix and interstitial fluid. Anisotropy in the hyperelastic behaviour has been formulated by means of a strain energy function that takes into account the influence of collagen fibres. Several numerical examples are shown in order to validate the proposed model. The confined compression problem has been solved to demonstrate the improvement that an Augmented Lagrangian Method provides with respect to a penalty approach. On the other hand, the unconfined compression problem allowed us to study the load distribution in each phase and its dependence on the strain rate. Finally, one realistic application of this model is briefly d