A large strain finite element analysis of cartilage deformation with electrokinetic coupling

We analyze the deformation of cartilage as a mixture of porous solid and fl uid and include additional effects due to swelling pressure. The swelling p ressure effects are interpreted through changes in water content, or local ion concentration, or electrokinetic coupling. The governing equations cons ist of the conservation of both solid and fluid linear momentum and the flu id continuity equations. Additional effects are governed by the relations, which encompass Ohm's and Darcy's laws for the electrokinetic coupling, or through the corresponding constitutive relation for swelling pressure. We c onsider the large deformations of solid by using logarithmic strains and fl uid velocity relative to the solid. We also take into account the change of porosity during deformation of the mixture. The governing equations are tr ansformed to the corresponding finite element relations by the standard Gal erkin procedure. In the incremental-iterative solution procedure, we includ e changes of geometry through an updated Lagrangian formulation. The propos ed general formulation is applied to problems solved theoretically and/or e xperimentally investigated. We demonstrate differences between solutions wh en small strain and large strain formulations are used. Material constants are determined form the numerical and analytical solutions, or estimated fr om experimental data. Differences in material constants, as a result of the approach in the numerical analysis, are discussed. (C) 2001 Elsevier Scien ce B.V. All rights reserved.