Effect of shape and interpenetration of ellipsoidal pores on effective physical properties of closed-cell porous materials

The purpose of this study is to clarify the effects of pore shape and interpenetration on the effective elastic modulus and thermal conductivity of closed-cell porous materials. For this purpose, the theoretical solutions for these effective physical properties of a model with ellipsoidal pores oriented randomly in the matrix are derived based on some homogenization methods such as the differential scheme (DS). The obtained solutions are expressed uniformly in terms of the geometrical factors given only by the aspect ratio of ellipsoidal pores. In addition, a model in which ellipsoidal pores are not only oriented randomly in the material but also interpenetrating is generated using the regular polyhedron orientation method associated with the golden ratio. Finite element method (FEM) analyses of this model are also performed. The effective physical properties of various closed-cell porous materials are calculated by the theoretical solutions and FEM. These results are compared with the experimental ones. When spherical pores do not interpenetrate, the DS results for effective physical properties show good agreement with the experimental and FEM results. However, when spherical pores interpenetrate, the DS results tend to be slightly higher than these results. This difference becomes negligible when the pore volume fraction is less than 0.5. Moreover, when the pore shape is non-spherical, such as elongated or flattened, the effect of interpenetration is reduced. As a result, the DS results show good quantitative agreement with the FEM results. These findings demonstrate that the DS can evaluate the effective physical properties of porous materials with a certain degree of accuracy, regardless of the shape and interpenetration of pores. The effective Young’s modulus and thermal conductivity tend to be highest when the pore shape is spherical and decrease as the pore shape becomes flatter. As an application of these findings, we present design guidelines for hybrid porous materials that improve insulation while maintaining stiffness.