Effective thermo-mechanical properties of compliant solids with small compressible liquid inclusions

While liquid-filled porous materials widely exist in both natural and engineering fields, their overall thermo-mechanical behaviors are influenced by the combined effects of solid skeleton, pore-filling liquid, and pore structure. When the pores are sufficiently small (e.g., micro/nano-scale pores), surface effects also play a significant role. Accounting for surface effects and liquid compressibility, we develop a theoretical model to predict the effective thermo-mechanical properties of liquid-filled porous materials. Idealized spherical compressible liquid inclusions distributed randomly in an elastic solid matrix are considered, with two scenarios separately considered. In the first scenario, the liquid inclusions are isolated so that the liquid does not flow freely. The effective coefficient of thermal expansion (CTE) and effective bulk modulus of the two-phase material are obtained via the generalized self-consistent method. In the second scenario, the liquid inclusions are connected by microchannels. We adopt a top-down approach (the mixture theory) to establish general thermo-mechanical constitutive relations for liquid-filled porous materials with surface effects, and then use a bottom-up (micromechanics) approach to determine the coupling coefficients (effective thermo-mechanical parameters) in these constitutive relations. Results show that the presence of surface stress at the solid-liquid interface increases the effective CTE and decreases the effective bulk modulus, especially when liquid compressibility is relatively large; however, the decrease in surface stress caused by increasing temperature weakens such effect. This research not only reveals the mechanism of thermo-mechanical coupling in liquid-filled porous materials having small pores but also provides a theoretical basis for accurate prediction of their thermo-mechanical responses in complex load environments.