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 $\sigma$ 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, ${\sigma }^{sk}$. For the given overall stress $\sigma$ and the computed value of the effective stress ${\sigma }^{sk}$, the effective stress supported by the fluid $P_{eff}$ is computed as the difference $\sigma -{\sigma }^{sk}$. Each of the two steps requires a solution to a boundary value problem which is solved numerically with the help of Python bvp solver.

本文是关于流体在支撑施加于非线性弹性流体饱和多孔材料的总压应力中的作用。考虑大变形和可压缩的超弹性基体材料的情况。由于问题的复杂性，将对多孔介质的简单模型进行详细研究，该模型由一组充液的气缸组成。在承受总应力的情况下，计算圆柱体固相和流体之间的应力分配的过程包括两个步骤。第一步，径向应力$\sigma$将给定大小的σ应用于流体填充缸的外半径，并确定径向位移。在第二步骤中，圆柱体的外表面的位移与第一步相同，但是圆柱体的腔是空的。第二步中作用于圆柱体外边界的径向应力定义为多孔介质固体骨架中的有效应力，${\sigma }^{sķ}$。对于给定的整体压力$\sigma$ 和有效应力的计算值 ${\sigma }^{sķ}$，由流体支撑的有效应力 $P_{ËFF}$ 计算为差异 $\sigma -{\sigma }^{sķ}$。这两个步骤的每一个都需要一个边界值问题的解决方案，该问题可以借助Python bvp求解器进行数值求解。