A cuboidal open cell model for constitutive modeling of surface effects in fluid-saturated porous materials

Fluid-saturated porous elastic materials, made up of connected networks of solid ligaments and characteristically having open pores, are commonly found in geological, biological and engineering materials. Surface effects can affect significantly the mechanical performance of such porous materials at macro scale, especially when the solid ligaments and the pores have micro or nano scale sizes. In the present study, in order to explicitly link pore-level geometrical parameters and surface effects with effective poroelastic properties as well as constitutive equations governing poroelastic deformation, we combine the top-down homogenization approach presented a previous study (Chen et al., 2021) with the bottom-up micromechanics approach. Inspired by the Gibson-Ashby cubic cell model for open-cell foams and the cellular networks typically found in fluid-saturated porous materials, we propose a cuboidal open cell model, with surface effects and fluid compressibility accounted for. For two limiting cases, i.e., the undrained state and the drained state, we demonstrate that both the surface moduli and residual surface stress (i.e., surface tension) prevent the deformation of solid ligaments, thus stiffening the porous material with enlarged effective Young's moduli. Further, we reveal that the two surface effect parameters (i.e., residual surface stress versus surface moduli) exhibit a coupling effect on effective moduli: when one parameter is large enough, the variation of the other affects significantly the effective moduli. As applications of the proposed model, we characterize mechanical behaviors of the porous material under typical loadings (e.g., uniaxial and non-proportional multiaxial tension) in both undrained and drained states; we also describe, for the first time, the stress concentration of a compressible liquid inclusion (e.g., a cell) with surface tension embedded in a fluid-saturated porous material with surface effects. Results of this study are beneficial for understanding and investigating how surface effects influence the poroelastic parameters of fluid-saturated porous materials having sufficiently small open pores.