Effective elastic properties of randomly distributed void models for porous materials

Abstract

Many 2D analytical models are available for estimating the effective elastic properties of porous materials. Most of these models adopt circular voids of a uniform diameter in superlattice arrays, such as unit void or periodically positioned models. There are two principal issues in a realistic representation of porous materials: the random distribution of a statistically sufficiently large number of voids in the model, and the random distribution of the size and position of the voids. Numerical schemes such as the FEM or the BEM have also been presented to cater for regular patterned circular voids. However, due to the large number of elements needed to produce sufficient accuracy for the curved boundary of circular voids or modelling a statistically sufficient number of voids with a random distribution in both the void size and the position, no such model has yet been produced. Modelling based on an FEM approach using a simplified approximation for void geometry is proposed here for the calculation of the effective elastic properties of porous solids. A plane strain model of a square geometry is adopted for a 2D array of voids. This simplified square shape allows a large number of voids to be simulated with a random distribution for both void sizes and their locations. The problem of anisotropy, which arises from the square shape, is discussed. It is verified that along the two principal directions (parallel to the sides of the square voids), the elastic properties remain the same as those predicted by using a circular void geometry. This square-shaped approximation, with its reduced requirement for FE analysis, has the potential to be extended to 3-dimensional modelling for a realistic simulation of engineering materials.