On the modelling of two-phase media by the finite element method

The equations of motion of a mixture of a solid and fluid are derived from the mixture theory of Truesdell and Toupin. These equations are based on the principles of balance of momentum, angular momentum, and mass. An elastoplastic constitutive model that includes kinematic hardening is implemented with the equations of motion to complete the description of the behavior of the solid phase. The compressibility of the liquid phase is included in the equation of conservation of mass. A finite element discretization of the governing equations of motion is obtained by applying the Galerkin method starting with a linear elastic phase. The finite element equations are extended for the case of a quasi-linear elastoplastic solid phase; these equations are solved by a Newton-Rhapson iteration which is performed at each time increment of the implicit Newmark integration method. This integration is proven to be numerically stable by applying mathematical theorems. The numerical scheme is coded by developing a FEM computer program that is adapted to solve boundary value problems related to experiments performed in the centrifuge in order to understand the physical coupling between the deformation of the solid phase and the development of pore pressures. The agreement between the experimental results and the theoretical predictions is consistent and reveals the nature and the effect of the parameters of the constitutive model on the coupling between the two phases of the mixture.