Mixed finite element modelling of cartilaginous tissues

Swelling and shrinking of cartilaginous tissues is modelled by a four-component mixture theory. This theory results in a set of coupled non-linear partial differential equations for the electrochemical potentials and the displacement. For the sake of local mass conservation these equations are discretised in space by a mixed finite element method. Integration in time by backward Euler leads to a non-linear system of algebraic equations. A subtle solution strategy for this system is proposed and tested for one-dimensional situations.