A mixed finite element formulation of triphasic mechano-electrochemical theory for charged, hydrated biological soft tissues

An equivalent new expression of the triphasic mechano-electrochemical theory [9] is presented and a mixed "nite element formulation is developed using the standard Galerkin weighted residual method. Solid displacement us, modi,ed electrochemical/chemical potentials e8, e`and e~ (with dimensions of concentration) for water, cation and anion are chosen as the four primary degrees of freedom (DOFs) and are independently interpolated. The modi"ed Newton}Raphson iterative procedure is employed to handle the non-linear terms. The resulting "rst-order Ordinary Di!erential Equations (ODEs) with respect to time are solved using the implicit Euler backward scheme which is unconditionally stable. One-dimensional (1-D) linear isoparametric element is developed. The "nal algebraic equations form a non-symmetric but sparse matrix system. With the current choice of primary DOFs, the formulation has the advantage of small amount of storage, and the jump conditions between elements and across the interface boundary are satis"ed automatically. The "nite element formulation has been used to investigate a 1-D triphasic stress relaxation problem in the con"ned compression con"guration and a 1-D triphasic free swelling problem. The formulation accuracy and convergence for 1-D cases are examined with independent "nite di!erence methods. The FEM results are in excellent agreement with those obtained from the other methods