A finite deformation theory and finite element formulation for coupled electrokinetic and fluid flow in soft tissues: Application to elecroosmotic flow

摘要

Due to the fixed charge density (FCD) in the solid matrix and the ionic nature of the interstitial fluid, cartilage and other soft tissues exhibit coupling between mechanical (deformation, fluid flow, fluid pressurization) and electrical (current, streaming potential) phenomena (Maroudas et al., 1969; Frank and Grodzinsky, 1987). Similar behavior has long been recognized in soil mechanics, and linear finite element formulations have been developed (Lewis and Garner, 1972). Soft tissues, however,typically undergo large deformations and have material properties that strongly vary with deformation. To date, no finite element formulations have been introduced that are capable of representing the nonlinear, electromechanically coupled behavior ofsoft tissues.In the current study, we formulated a nonlinear, variationally derived finite deformation theory for coupled electrokinetic and poroelastic phenomena in cartilage and other porous media. This formulation includes three vector fields representing solid and fluid motion and current flow, as well as two scalar fields representing the fluid pressure and electrical potential. An axisymmetric finite element implementation of the theory was used to investigate electroosmotic flow across homogeneous andinhomogeneous specimens.