Reference: A.P. Roberts and E.J. Garboczi, J. Mech. Phys. Solids 50 (1), 33-55 (2002).

(PDF Version of Original paper)

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Elastic properties of model random three-dimensional open-cell solids


1Building Materials Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
2Centre for Microscopy and Microanalysis, University of Queensland, St. Lucia, Queensland 4066, Australia


Most cellular solids are random materials, while practically all theoretical results are for periodic models. To be able 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 ( $\rho$ ) and microstructure dependence of the Young's modulus (E) and Poisson's ratio ($\nu$) for four different isotropic random models. The models were based on Voronoi tessellations, level-cut Gaussian random fields, and nearest neighbour 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  $E\propto\rho^n$ n. 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=2. The observed variance in the exponent was found to be consistent with experimental data. We found that the Voronoi tessellation model, which is often used as a common model of isotropic foamed solids, exhibits incompressibility ($\nu$   ½) at low densities. This behaviour is not 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 reproduce the experimental Poisson's ratio.

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