Penalty finite element method for nonlinear dynamic response of viscous fluid-saturated biphase porous media

The governing equations as well as boundary and initial conditions for nonlinear dynamic response problems of viscous fluid_saturated biphase porous medium model, based on mixture theory, are presented. With Galerkin weighted residual method the corresponding nonlinear dynamic penalty finite element equation, in which the dependencies of volume fraction and permeation coefficients on deformation are included, is obtained. The iteration solution method of the nonlinear system equation is also discussed. As a numerical example, the dynamic response of a porous medium column under impulsive loading action is analyzed with the developed finite element program. The numerical results demonstrate the efficiency and correctness of the method.