A finite element solution procedure for porous medium with fluid flow and electromechanical coupling
✍ Scribed by Kojic, Milos ;Filipovic, Nenad ;Vulovic, Snezana ;Mijailovic, Srboljub
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 241 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1069-8299
No coin nor oath required. For personal study only.
✦ Synopsis
We consider a coupled problem of the deformation of a porous solid, ¯ow of a compressible ¯uid and the electrical ®eld in the mixture. The governing equations consist of balance of the linear momentum of solid and of ¯uid, continuity equations of the ¯uid and current density, and a generalized form of Darcy's law which includes electrokinetic coupling. The compressibility of the solid and the ¯uid are taken into account. We transform these equations to the corresponding ®nite element relations by employing the principle of virtual work and the Galerkin procedure. The nodal point variables in our general formulation are displacements of solid, ¯uid pore pressure, relative velocity of the ¯uid 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 boundary conditions for the solid, relative velocity of the ¯uid, ¯uid pressure, current density and electrical potential. The dynamic-type non-symmetric system of equations is solved through the Newmark procedure, while in the case of neglect of inertial terms we use the Euler method.
Numerical examples, solved by our general-purpose FE package PAK, are taken from biomechanics. The results are compared with those available in the literature, demonstrating the correctness and generality of the procedure presented.