A FINITE-ELEMENT SOLUTION PROCEDURE FOR POROUS-MEDIUM WITH FLUID-FLOWAND ELECTROMECHANICAL COUPLING

We consider a coupled problem of the deformation of a porous solid, fl ow of a compressible fluid and the electrical field in the mixture. Th e governing equations consist of balance of the linear momentum of sol id and of fluid, continuity equations of the fluid and current density , and a generalized form of Darcy's law which includes electrokinetic coupling. The compressibility of the solid and the fluid are taken int o account. We transform these equations to the corresponding finite el ement relations by employing the principle of virtual work and the Gal erkin procedure. The nodal point variables in our general formulation are displacements of solid, fluid pore pressure, relative velocity of the fluid and electrical potential. Derivation of the FE equations is presented for small displacements and elastic solid, which can further be generalized to large displacements and inelastic behaviour of the solid skeleton. According to this formulation we can include general b oundary conditions for the solid, relative velocity of the fluid, flui d pressure, current density and electrical potential. The dynamic-type non-symmetric system of equations is solved through the Newmark proce dure, while in the case of neglect of inertial terms we use the Euler method. Numerical examples, solved by our general-purpose FE package P AK, are taken from biomechanics. The results are compared with those a vailable in the literature, demonstrating the correctness and generali ty of the procedure presented. (C) 1998 John Wiley & Sons, Ltd.