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

We analyze the deformation of cartilage as a mixture of porous solid and fluid and include additional effects due to swelling pressure. The swelling pressure effects are interpreted through changes in water content, or local ion concentration, or electrokinetic coupling. The governing equations consist of the conservation of both solid and fluid linear momentum and the fluid continuity equations. Additional effects are governed by the relations, which encompass Ohmʹs and Darcyʹs laws for the electrokinetic coupling, or through the corresponding constitutive relation for swelling pressure. We consider the large deformations of solid by using logarithmic strains and fluid velocity relative to the solid. We also take into account the change of porosity during deformation of the mixture. The governing equations are transformed to the corresponding finite element relations by the standard Galerkin procedure. In the incremental-iterative solution procedure, we include changes of geometry through an updated Lagrangian formulation. The proposed general formulation is applied to problems solved theoretically and/or experimentally investigated. We demonstrate differences between solutions when small strain and large strain formulations are used. Material constants are determined form the numerical and analytical solutions, or estimated from experimental data. Differences in material constants, as a result of the approach in the numerical analysis, are discussed.