TRIPHASIC FINITE-ELEMENT MODEL FOR SWELLING POROUS-MEDIA

The equations describing the mechanical behaviour of intervertebral di sc tissue and other swelling porous media are three coupled partial di fferential equations in which geometric and physical non-linearities o ccur. The boundary conditions are deformation-dependent. To solve the equations for an arbitrary geometry and arbitrary boundary conditions, we use the finite element (FE) method. The differential equations are rewritten in an integral form by means of the weighted residual metho d. The domain of the integral is defined via a set of shape functions (i.e. finite elements). By applying the Gauss theorem and rewriting wi th respect to the reference state (total Lagrange), non-linear equatio ns are obtained. These are solved by means of the Newton-Raphson techn ique. In order to get a finite set of equations, the weighted residual equations are discretized. The shape functions are chosen as weightin g functions (Galerkin method). This discretization results in a non-sy mmetric stiffness matrix. A general description is given for the eleme nts implemented into the commercial FE package DIANA (DIANA Analysis B .V., Delft, Netherlands). The numerical results of unconfined compress ion of a schematic intervertebral disc with varying proteoglycan conce ntration are given.