A mixed stabilized finite element formulation for finite deformation of a poroelastic solid saturated with a compressible fluid

A stabilized finite element formulation is proposed to the study of the finite deformation of a porous solid saturated with a compressible fluid. Unlike previous finite element schemes, the compressibility of the fluid constituent is entirely considered, and particularly, the a porosity-dependent permeability is utilized in the present formulation. As a special case, the formulation for the saturating fluid being an ideal gas is also derived. The displacement of solid skeleton and pore pressure are treated as primary variables to express the resulting coupled nonlinear system of equations. Equal-order \(C^{0}\) elements are employed to approximate displacement and pressure fields. The stability problem caused by the equal-order interpolation is overcome by using the method of polynomial pressure projections. Two examples are provided to demonstrate the effect of fluid compressibility, as well as the porosity-dependent permeability, on the responses of the material.