An ultra-simple universal model for the effective elastic properties of isotropic 3D closed-cell porous materials

In this paper, effective elastic properties of the isotropic 3D closed-cell porous materials are comprehensively investigated through finite element method simulations, theoretical formulations and experimental tests. 3D representative volume element models with randomly distributed non-overlapping Voronoi-structured voids of various porosities (from 0.01 to 0.99) are created to compute the effective bulk and shear moduli of the porous materials. An ultra-simple universal model (USUM) is developed to predict the effective shear modulus covering the entire porosities. The effective Young's modulus and Poisson's ratio of ultra-simple form are then formulated. The findings show that the theoretical estimates agree well with the numerical results for all the effective elastic properties. The uniaxial compression tests are implemented on the specimens of 3D printed porous nylon to measure the effective Young's modulus. The results suggest that the theoretical predictions of the USUM agree very well with the effective Young's moduli of the porous materials, covering a wide range of porosity.