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

Abstract

Porous materials are formed in nature and by man by many differentprocesses. The nature of the pore space, which is usually the space leftover as the solid backbone forms, is often controlled by the morphology ofthe solid backbone. In particular, sometimes the backbone is made from therandom deposition of elongated crystals, which makes analytical techniquesparticularly difficult to apply. This paper discusses simple two- andthree-dimensional porous models in which the solid backbone is formed by differentrandom arrangements of elongated solid objects (bars/crystals). We use ageneral purpose elastic finite element routine designed for use on imagesof random porous composite materials to study the linear elastic propertiesof these models. Both Young's modulus and Poisson's ratio depend on theporosity and the morphology of the pore space, as well as on the propertiesof the individual solid phases. The models are random digital image models,so that the effects of statistical fluctuation, finite size effect anddigital resolution error must be carefully quantified. It is shown how toaverage the numerical results over random crystal orientation properly. Therelations between two and three dimensions are also explored, as mostmicrostructural information comes from two-dimensional images, while mostreal materials and experiments are three dimensional.