Abstract
Conventional analytical formulas for predicting the effective Young's modulus of porous materials often rely on simplifying assumptions and do not explicitly incorporate microstructural information. This study investigates the impact of regular versus irregular pore distributions on the stiffness of porous materials using microstructure-free finite element modeling (MF-FEM). After conducting a convergence study, MF-FEM predictions were validated against experimental data and used to assess the accuracy of commonly employed analytical models. The results demonstrate that materials with irregular microstructures exhibit a rapid decrease in Young's modulus, approaching zero at porosities slightly greater than 50%. In contrast, regular microstructures show a more gradual decline, maintaining significant stiffness until the porosity exceeds 90%. Additionally, the study reveals that some analytical formulas align better with irregular microstructures while others are more suited to regular ones, attributable to the underlying assumptions of these models. These findings underscore the necessity of considering pore distribution patterns in modeling to accurately predict the mechanical behavior of porous materials.