Linear elastic properties of 2D and 3D models of porous materials made from elongated objects

Porous materials are formed in nature and by man by many different processes. The nature of the pore space, which is usually the space left over as the solid backbone forms, is often controlled by the morphology of the solid backbone. In particular, sometimes the backbone is made from the random deposition of elongated crystals, which makes analytical techniques particularly difficult to apply. This paper discusses simple two- and three-dimensional porous models in which the solid backbone is formed by different random arrangements of elongated solid objects (bars/crystals). We use a general purpose elastic finite element routine designed for use on images of random porous composite materials to study the linear elastic properties of these models. Both Young's modulus and Poisson's ratio depend on the porosity and the morphology of the pore space, as well as on the properties of the individual solid phases. The models are random digital image models, so that the effects of statistical fluctuation, finite size effect and digital resolution error must be carefully quantified. It is shown how to average the numerical results over random crystal orientation properly. The relations between two and three dimensions are also explored, as most microstructural information comes from two-dimensional images, while most real materials and experiments are three dimensional.