Finite Swelling with Weakly Fulfilled Boundary Conditions

Biological soft tissues exhibit a swelling behaviour and consist of multiple phases, a solid phase composed of collgagen fibers and charged PGA chains and a fluid phase composed of the liquid solvent and the ions of dissolved salt.

In this contribution, the Theory of Porous Media (TPM) model consists of four constituents, a charged solid and an aqueous solution composed of water and the ions of dissolved salt. The solid is modelled by a finite elasticity law accounting for the multiphasic micro structure, whereas the fluid is considered as a viscous Newtonian fluid. One finally ends up with the volume balance of the fluid, the concentration balance of the cations, the momentum balance of the overall mixture. The resulting set of partial differential equations is solved within the framework of the FEM. Therefore, the weak forms are derived and the resulting set of equations for the primary variables pore pressure p, cation concentration c and solid displacement u_S , is implemented into the FE tool PANDAS. Finally, a three dimensional example of a swelling hydrogel disc is shown. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)