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

Most cellular solids are random materials, while practically all theoretical structure-property relations are tor 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 ( I J ) and microstructure dependence of the Young's modulus ( E ) and Poisson's ratio ( v ) for four different isotropic random models. The models were based o n 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. A t low densities. the Young's modulus can be described by the relation E x p". 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 cxponent was found to be consistent with experimental data. A t low densities we found that = 0.25 for three of the four models studied. In contrast, the Voronoi tessellation. which is a common model of foams. became approximately incompressible (1' =: 0.5 ). This behaviour is not commonly observed experimentally. Our studies showed the result was robust to polydispersity and that a relatively large number ( 1 5 O h ) of the bonds must be broken to significantly reduce the low-density Poission's ratio to 1 ' 2 0.33. C 2001 Elsevier Science Ltd. All rights reserved. K r ~ ~ i w r d s . Structure-property relationships; .A. Microstructures; B Foam material: C . Finite elements: C'. Probability and statistics Corresponding author. Permanent a d d r e s Centre tor Llicroscopy and Microanalysis. University of Queensland. St. Lucia. Queensland 4077. Australia. Tel: -6 l-7-3365-.4Yq?; fax: -6 1-7-3365-4422. E-mui/ trddrc,w 3nthony.roberrsru:mailbox.uq.sdu.3u i .A.P. Robens).