Effects of cell shape and strut cross-sectional area variations on the elastic properties of three-dimensional open-cell foams

The Voronoi tessellation technique and the finite element method are utilized to investigate the microstructure-property relations of three-dimensional (3-D) cellular solids (foams) that have irregular cell shapes and non-uniform strut cross-sectional areas (SCSAs). Perturbations are introduced to a regular packing of seeds to generate a spatially periodic Voronoi diagram with different degrees of irregularity (amplitude a), and to the constant SCSA to generate a uniform distribution of SCSAs with different degrees of non-uniformity (amplitude b). Twenty finite element (FE) models are constructed, based on the Voronoi diagrams for twenty foam samples (specimens) having the same pair of a and 6, to obtain the mean values and standard deviations of the elastic properties. Each of these specimens contains 125 cells. Spatially periodic boundary conditions are applied to each specimen. This differs from most of the existing studies, where displacement boundary conditions are typically employed. The simulation results indicate that, on average, the variations of cell shapes and SCSAs have appreciable effects on the elastic moduli but insignificant influence on the Poisson's ratios. For low-density imperfect foams, the elastic moduli increase as cell shapes become more irregular, but decrease as SCSAs get less uniform. When the relative density (R) increases, the elastic moduli of imperfect foams increase substantially, while the Poisson's ratios decrease moderately. The effect of the interaction between the two types of imperfections on foam elastic properties appears to be weak. The disparity between the elastic properties in three orthogonal directions for the 3-D imperfect foams is found to be negligibly small regardless of the values of a, b and R and the shapes of strut cross sections, which indicates that such foams can be regarded as Isotropic. Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.