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.Comment: 13 pages, 13 figure

A reaction-diffusion model for the hydration/setting of cement

We propose a heterogeneous reaction-diffusion model for the hydration and setting of cement. The model is based on diffusional ion transport and on cement specific chemical dissolution/precipitation reactions under spatial heterogeneous solid/liquid conditions. We simulate the spatial and temporal evolution of precipitated micro structures starting from initial random configurations of anhydrous cement particles. Though the simulations have been performed for two dimensional systems, we are able to reproduce qualitatively basic features of the cement hydration problem. The proposed model is also applicable to general water/mineral systems.Comment: REVTeX (12 pages), 4 postscript figures, tarred, gzipped, uuencoded using `uufiles', coming with separate file(s). Figure 1 consists of 6 color plates; if you have no color printer try to send it to a black&white postscript-plotte

Elastic properties of a tungsten-silver composite by reconstruction and computation

We statistically reconstruct a three-dimensional model of a tungsten-silver composite from an experimental two-dimensional image. The effective Young's modulus ($E$) of the model is computed in the temperature range 25-1060^o C using a finite element method. The results are in good agreement with experimental data. As a test case, we have reconstructed the microstructure and computed the moduli of the overlapping sphere model. The reconstructed and overlapping sphere models are examples of bi-continuous (non-particulate) media. The computed moduli of the models are not generally in good agreement with the predictions of the self-consistent method. We have also evaluated three-point variational bounds on the Young's moduli of the models using the results of Beran, Molyneux, Milton and Phan-Thien. The measured data were close to the upper bound if the properties of the two phases were similar ($1/6 < E_1 /E_2 < 6$).Comment: 23 Pages, 12 Figure