Role of fluid phase in compression of nonlinear elastic fluid-saturated porous medium

Abstract

This paper is about the role of the fluid in supporting the overall compressive stress applied to nonlinear elastic fluid-saturated porous material. The case of large deformation and compressible hyperelastic matrix material is considered. Due to complexity of the problem, a simple model of the porous medium consisting of an assemblage of fluid-filled cylinders is studied in more detail. The procedure for computing the stress partitioning between the solid phase of the cylinder and the fluid in withstanding the overall stress consists of two steps. In the first step, the radial stress σ of given magnitude is applied to outer radius of the fluid-filled cylinder and the radial displacement is determined. In the second step, the displacement of the outer surface of the cylinder is equal to that of the first step but the cavity of the cylinder is empty. The radial stress acting on the outer boundary of the cylinder in the second step is defined as an effective stress in the solid skeleton of the porous medium, σsk. For the given overall stress σ and the computed value of the effective stress σsk, the effective stress supported by the fluid Peff is computed as the difference σ−σsk. Each of the two steps requires a solution to a boundary value problem which is solved numerically with the help of Python bvp solver.