A nonlinear finite element formulation for axisymmetric torsion of biphasic materials

In this paper, we present a finite element formulation for describing the large deformation torsional response of biphasic materials, with specific application to prediction of nonlinear coupling between torsional deformation and fluid pressurization in articular cartilage. Due to the use of a cylindrical coordinate system, a particular challenge arises in the linearization of the weak form. The torsional axisymmetric case considered gives rise to additional geometric terms, which are important for the robustness of the numerical implementation and that would not be present in a Cartesian formulation. A detailed derivation of this linearization process is given, couched in the context of a variational formulation suitable for finite element implementation. A series of numerical parametric studies are presented and compared to experimental measurements of the time dependent response of cartilage.