Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three–dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, &ngr;s, over the entire solid fraction range, and Poisson's ratio, &ngr;, becomes independent of &ngr;s as the percolation threshold is approached. We represent this behaviour of &ngr; in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two–dimensional porous materials. In addition, the behaviour of &ngr; versus &ngr;s appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite–element results in terms of simple structure–property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate– to high–porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.