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.

流体饱和的多孔弹性材料，由连接的固体韧带网络组成，具有开孔特征，在地质、生物和工程材料中很常见。表面效应会在宏观尺度上显着影响此类多孔材料的机械性能，尤其是当固体韧带和孔隙具有微米或纳米尺度时。在本研究中，为了明确地将孔隙级几何参数和表面效应与有效多孔弹性特性以及控制多孔弹性变形的本构方程联系起来，我们结合了先前研究中提出的自上而下均质化方法（Chen 等人，2021 年） ) 采用自下而上的微观力学方法。受开孔泡沫的 Gibson-Ashby 立方单元模型和通常在流体饱和多孔材料中发现的蜂窝网络的启发，我们提出了一个立方体开孔模型，其中考虑了表面效应和流体可压缩性。对于两个极限情况，即，在未排水状态和排水状态下，我们证明了表面模量和残余表面应力（即表面张力）可防止固体韧带变形，从而使多孔材料变硬，有效杨氏模量增大。此外，我们揭示了两个表面效应参数（即残余表面应力与表面模量）对有效模量表现出耦合效应：当一个参数足够大时，另一个参数的变化会显着影响有效模量。作为所提出模型的应用，我们描述了多孔材料在典型载荷下的力学行为（例如，单轴和非比例多轴拉伸）在不排水和排水状态下；我们还首次描述了具有表面张力的可压缩液体内含物（例如细胞）的应力集中，该内含物嵌入具有表面效应的流体饱和多孔材料中。这项研究的结果有助于理解和研究表面效应如何影响具有足够小开孔的流体饱和多孔材料的孔隙弹性参数。