MATHEMATICAL MODELING OF THE MECHANICAL BEHAVIOR OF AN ARTICULAR CARTILAGE PIECE

The articular cartilage is a poroelastic biological material that allows the distribution of mechanical loads and the joint movements. As a biphasic material, in presence of load, the articular cartilage deform its solid matrix and modifies the fluid hydrostatic pressure inside. The aim of this work is to implement numerically a mathematical model that predicts the mechanical behaviour of articular cartilage taking into account the duality between the solid matrix and articular liquid, and its poroelastic feature. Using a finite element method approach, the response of a piece of articular cartilage in one and two dimensions has been simulated, with tensile, compresive and oscillative mechanical loads. The analysis of results allows a qualitatively validation of the poroelastic behavior of the model due to the solid matrix deformation and the fluid outflow that causes variations of pressures inside the articular cartilage according with reported trials. We conclude that the mathematical model allows the prediction of the articular cartilage biomechanical behaviour. Our results contribute to the investigative processes in fields of study like biomechanics and tissue engineering.