Mechanical behaviors of closed-cell fluid-filled porous media with surface effects

The mechanical behaviors of closed-cell fluid-filled porous media (CFPM) with surface effects between fluid and solid matrix have been attracting researchers’ interest over the past decades. However, current theoretical and numerical methods mainly focus on the small deformation behaviors of the CFPM with uniform pore size, while neglecting several important features, such as the non-uniform distribution of pore sizes and finite deformation. These features, which are common in engineering materials like foams and soft composites, play a crucial role in their overall performance. In this paper, we propose a user-friendly simulation method in the commercial finite element software Comsol based on the weak form formulation of the problem with surface effects incorporated. We validate this method by comparing it with the theoretical solution of the deformation near a single fluid inclusion with surface effects. Predictions of our model demonstrate that surface tension inhibits the deformation of the fluid inclusion, resulting in three distinct states: normal state, growth state, and shrinkage state. Next, we employ a homogenization method to develop an approximate theoretical solution for dual-scale CFPM and examine their equivalent mechanical properties. The shear modulus of dual-scale CFPM is influenced by the compressibility of the internal fluids, in contrast to CFPM with single-sized pores. This effect arises primarily from the different deformation modes of pores at varying scales with the same surface tension, which is verified by the two-level homogenization solution. We also examined the mechanical properties of CFPM with Gaussian-distributed pore sizes, finding that surface effects are inhibited compared to single-pore-size CFPM, especially as the standard deviation of pore radii increases. Finally, we investigated the industry challenge of finite deformation of CFPM with surface effects, the approach demonstrates that the Neo-Hookean model predicted by the microstructure, based on existing effective moduli, remains accurate up to 50% strain for multiple loading cases. These results provide theoretical support and technical guidance for engineers in structural design, process optimization, and performance prediction of CFPM.