An Ultra-Simple Universal Model for the Effective Elastic Properties of 3D Closed-Cell Porous Materials

Abstract

In this paper, effective elastic properties of the 3D closed-cell porous materials are comprehensively investigated through finite element method (FEM) simulations, theoretical formulations and experimental tests. 3D representative volume element (RVE) models with randomly distributed non-overlapping Voronoi-structured voids of various porosities (from 0.1 to 0.99) are created to compute the effective bulk and shear moduli of the porous materials. The numerical results show that the composite-sphere model (CSM) and the three-phase model (TPM) provide the best predictions of the effective bulk and shear moduli of the porous materials, respectively, for the entire range of porosity. Motivated by this result, an ultra-simple universal model (USUM) is developed based on a proper Taylor expansion of the TPM to predict the effective shear modulus. The effective Young's modulus and Poisson's ratio of ultra-simple form are then formulated based on the CSM and USUM. The findings show that the theoretical estimates agree well with the numerical results for all the effective elastic properties. The 3D printing technology is utilized to fabricate the porous nylon specimens with various porosities of closed-cells. The uniaxial compression tests are implemented to measure the effective Young's modulus of the porous nylon materials. The results suggest that the theoretical predictions of the ultra-simple form, formulated by the CSM and USUM, agree very well with the effective Young's moduli of the porous materials, covering a wide range of porosity.