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Elastic Properties of Model Random Three-Dimensional Open-Cell Solids



A P. Roberts, Edward Garboczi


Most cellular solids are random materials, while practically all theoretical structure-property relations are for periodic models. To generate theoretical results for random models the finite element method (FEM) was used to study the elastic properties of open-cell solids. We have computed the density (ρ) and microstructure dependence of the Young's modulus (E) and Poisson's ratio (Ņ) for four different isotropic random models. The models were based on Voronoi tessellations, level-cut Gaussian random fields, and nearest neighbor node-bond rules. These models were chosen to broadly represent the structure of foamed solids and other (non-foamed) cellular materials. At low densities, the Young's modulus can be described by the relation E ∝ ρn. The exponent n and constant of proportionality depend on microstructure. We find 1.3 < n < 3, indicating a more complex dependence than indicated by periodic cell theories, which predict n = 1 or 2. The observed variance in the exponent was found to be consistent with experimental data. At low densities we found that νnearly equal to} 0.25 for three of the four models studied. In contrast, the Voronoi tessellation, which is a common model of foams, became approximately incompressible (Ņnearly equal to} 0.5). This behavior is not commonly observed experimentally. Our studies showed the result was robust to polydispersity and that a relatively large number (15%) of the bonds must be broken to significantly reduce the low-density Poisson's ratio to Ņ nearly equal to} 0.33.
Journal of the Mechanics and Physics of Solids
No. 1


cellular solid, elastic moduli, finite element, foam, Gaussian random field, Poisson's ratio, random, Voronoi, Young's modulus


Roberts, A. and Garboczi, E. (2002), Elastic Properties of Model Random Three-Dimensional Open-Cell Solids, Journal of the Mechanics and Physics of Solids, [online], (Accessed May 18, 2024)


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Created December 31, 2001, Updated October 12, 2021