3D FE implementation of an incompressible quadriphasic mixture model

A quadriphasic mixture model, intended to apply to biological tissues, consists of a deforming solid saturated with a fluid, cations and anions. Governing equations of the model are shortly given. The coupled set of differential equations are solved in a finite element method using a weighted residual approach(updated Lagrange). A Newton-Raphson iteration scheme is applied for linearization of the non-linear set of equations. Interpolation functions are chosen equal to the weighting functions (Galerkin) in discretization.The FE model is then validated for small deformations using the analytical solutions for 1D confined consolidation and swelling. 3D effects are shown in a swelling cylindrical hydrogel sample