Elastic moduli of model random three-dimensional closed-cell cellular   solids
  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 solids with a closed-cell cellular structure. We have computed the density ($\rho$) and microstructure dependence of the Young's modulus ($E$) and Poisson's ratio (PR) for several different isotropic random models based on Voronoi tessellations and level-cut Gaussian random fields. The effect of partially open cells is also considered. The results, which are best described by a power law $E\propto\rho^n$ ($1 < n <2$), show the influence of randomness and isotropy on the properties of closed-cell cellular materials, and are found to be in good agreement with experimental data. 
Anthony Roberts, Ed Garboczi