Finite Element Modeling and Simulation of the Multiphysic Behavior of Articular Cartilage

Abstract The finite element method (FEM) is the most widely used numerical method for solving complex problems mathematically represented by one or several coupled field equations in continuum physics. The main power of the FEM appears in coupled, nonlinear, and heterogeneous problems where several physical fields interact pointwise in a nonlinear way. This is the case of the behavior of articular cartilage in animals and humans, where the stress distribution is coupled with the fluid flow around the solid matrix and the constitutive behavior is controlled by the complex interaction of the fluid pressure, the Donnan pressure induced by the internal electrical charges in the fluid and matrix, and, finally, the fiber collagen distribution in the solid matrix. These three problems (electrochemistry, solid mechanics, and fluid diffusion) are strongly coupled and contribute together to the characteristic swelling and viscoelastic behavior of this biological tissue, which, in turn, is critical in its physiological and pathological behaviors. In this chapter, the physicomathematical model of articular cartilage is described as well as the three-field problem discretization and solution by means of the FEM, including its implementation within the commercial FE software ABAQUS via a user-defined subroutine. Finally, several examples of clinical interest are solved and discussed with the objective of showing the main properties, pros and cons of this numerical technique in this complex problem.