Numerical modelling of cartilage as a deformable porous medium

Soft biological tissues, like cartilage and intervertebral disc tissue, exhibit swelling and shrinking behaviour due to mechanical and chemical loadings. A mixture theory is used to simulate this behaviour. First, the biphasic mixture theory is investigated. In this theory, the mechanical behaviour is described by mass and momentum balances, and constitutive equations. As a result a system of coupled, time-dependent, non-linear equations is obtained. These equations are discretised in space by a mixed-hybrid finite element method, and in time by a suitable implicit time integrator. Unlike the u- p formulation (the displacements and the fluid pressure are the unknowns), the mixed-hybrid finite element method yields a conservative velocity-field of the fluid, which is a sound basis for accurate computations of, for example, diffusion of particles inside the fluid. Then, the biphasic mixture theory is extended to a four components mixture theory in order to model chemical and electrical phenomena inside the material.