The processes that are used to form natural and man-made porous materials are diverse. Some are formed by introducing bubbles into a viscous liquid, then hardening the liquid, like in foaming processes. However, many porous materials are formed by building up a solid structure that incorporates empty areas into its overall body. In this case, the morphology of the pores, which are made up of the "left-over" space around the forming solid backbone, is mainly determined by the morphology of the solid products. This is the case for cement-based materials, which are among the most highly-used porous materials produced by mankind. One particular kind of cement-based material is gypsum plaster, widely used for the production of gypsum plaster board, of which billions of square meters are produced every year across the world. This material is an example of a porous solid made up from elongated gypsum crystals that randomly intersect and grow together from seeds to form a random porous solid. In general, there has been some success in using bounds, expansions, and effective medium theories to understand the effective properties of composite materials made up from inclusions in a matrix [ 1, 2]. However, these analytical theories are generally not terribly successful in describing the effective properties of microstructures made up from intersecting solid objects, and particularly elongated objects. Hence the need to turn to simple computer simulation models to help sort out these relationships.
Chapter 1 in Ref. [3] describes a "tool-kit" of computational methods that can be used on digital images of porous materials. One part of this collection of tools is a suite of finite element programs that can be used to explore many aspects of the linear elastic properties of random porous materials [4]. These can be used to quickly explore many different random models of random porous media, examining their effective elastic properties as a function of porosity and pore morphology. These numerical data can then be used to interpret and explain experimental data.
This paper is then a computational investigation of the linear elastic properties of various simple models for random porous materials made up from the random arrangement of solid elongated objects (bars). We investigate how the morphology of the solid and pore space affects the elastic properties, and how varying the solid properties affects the overall elastic properties. Comparisons between two dimensions (2-D) and three dimensions (3-D) are especially useful, because most microstructural information is obtained in 2-D, from images of various kinds, while the measurement of elastic properties is in 3-D. Also, because these are random digital models, the effects of statistical fluctuation, finite size effect, and digital resolution errors must be carefully quantified in order to ensure valid results. Comparison is made both to the elastic properties of other random models, and to measured elastic properties of real materials. The emphasis of this paper is on how solid and pore morphology affect elastic properties, and on how simple models can be used to help elucidate the phenomena found in real porous materials.