Comparison of a biphasic and a multicomponent model describing viscoelastic swelling phenomena

Biological soft tissues like articular cartilage and their artificial replacement hydrogel have a multicomponent microstructure, consisting of a charged viscoelastic solid matrix saturated by a fluid, which is composed of the liquid solvent and the dissolved anions and cations. Such charged multiphasic materials exhibit a swelling behaviour under varying chemical conditions. These materials are best described by a macroscopic approach like the Theory of Porous Media (TPM). Starting from this point, a standard two-phase model is extended by dividing the fluid into the above mentioned components. Therein, the chemical relations describing the behaviour of the ions and their interaction with the other mixture constituents are incorporated. The resulting model covers mechanical as well as osmotic and electrostatic effects. For numerical and simplicity reasons, it is possible to describe the swelling phenomena by a simplified biphasic model, where the ions as a third degree of freedom and their time-dependent diffusion are neglected. Furthermore, the viscoelastic solid matrix can be replaced by an elastic material. Note that using the multicomponent model generally results in numerical problems, since the boundary conditions depend on the internal fixed charge density. It is shown that this problem can be solved by including the boundary conditions into the weak formulation. Finally, to compare the different behaviour of the above mentioned models by means of an swelling example, they are implemented into the FE tool PANDAS using stable Taylor-Hood elements for the spatial discretization. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)