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 theor y [9] is presented and a mixed finite element formulation is developed usin g the standard Galerkin weighted residual method. Solid displacement u(s), modified electrochemical/chemical potentials epsilon(w), epsilon(+) and eps ilon(-) (with dimensions of concentration) for water, cation and anion are chosen as the four primary degrees of freedom (DOFs) and are independently interpolated. The modified Newton-Raphson iterative procedure is employed t o handle the non-linear terms. The resulting first-order Ordinary Different ial Equations (ODEs) with respect to time are solved using the implicit Eul er backward scheme which is unconditionally stable. One-dimensional (1-D) l inear isoparametric element is developed. The final algebraic equations for m a non-symmetric but sparse matrix system. With the current choice of prim ary DOFs, the formulation has the advantage of small amount of storage, and the jump conditions between elements and across the interface boundary are satisfied automatically. The finite element formulation has been used to i nvestigate a 1-D triphasic stress relaxation problem in the confined compre ssion configuration and a 1-D triphasic free swelling problem. The formulat ion accuracy and convergence for 1-D cases are examined with independent fi nite difference methods. The FEM results are in excellent agreement with th ose obtained from the other methods. Copyright (C) 1999 John Wiley & Sons, Ltd.