Reference: A.P. Roberts and E.J. Garboczi, Acta Materiala, 49, No. 2, pp. 189-197, (2001).

(PDF Version of Original Paper)

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Elastic moduli of model random three-dimensional closed-cell cellular solids

A. P. ROBERTS1,2 and E. J. GARBOCZI1
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

Abstract:

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 $E\propto\rho^n$ 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.

Keywords: 1. Foams, 2. Mechanical properties: elastic, 3. Micro-structure


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