Non-linear finite element analysis of mechanical electrochemical phenomena in hydrated soft tissues based on triphasic theory

The well-accepted triphasic theory for modelling the mechano-electrochemical phenomena of charged hydrated soft tissue has been limited to infinitesimal deformation problems due to the difficulty of defining a common reference configuration for the whole tissue. In this paper, an imaginary reference configuration for soft tissue under large deformation is established based on the reference configuration of a solid matrix and a Piola transformation of the relative velocities of the fluid and ionic phases. A non-linear finite element analysis formulation is proposed by applying a weighted residual method to the reformulated governing equations of triphasic theory reformulated in the imaginary reference configuration, with the displacement of the solid, fluid flows, ionic molar flows, hydrostatic pressure, and electrical potential as the unknown variables. After verifying the proposed finite-element formulation by comparing the results of a linear-confined compression problem with those obtained by the finite difference method, the numerical analysis of a three-dimensional free-swelling problem of articular cartilage with large deformation, and a strong non-linearity in the material properties is carried out to reproduce the curling behaviour of articular cartilage strips in vitro when submerged in solution baths of various concentrations. The results obtained by finite element analysis are in agreement with those measured experimentally