Random distribution of polydisperse ellipsoidal inclusions and homogenization estimates for porous elastic materials

Abstract

This work proposes an extension of the well-known random sequential adsorption (RSA) method in the context of non-overlapping random mono- and polydisperse ellipsoidal inclusions. The algorithm is general and can deal with inclusions of different size, shape and orientation with or without periodic geometrical constraints. Specifically, polydisperse inclusions, which can be in terms of different size, shape, orientation or even material properties, allow for larger volume fractions without the need of additional changes in the main algorithm. Unit-cell computations are performed by using either the fast Fourier transformed-based numerical scheme (FFT) or the finite element method (FEM) to estimate the effective elastic properties of voided particulate microstructures. We observe that an isotropic overall response is very difficult to obtain for random distributions of spheroidal inclusions with high aspect ratio. In particular, a substantial increase (or decrease) of the aspect ratio of the voids leads to a markedly anisotropic response of the porous material, which is intrinsic of the RSA construction. The numerical estimates are probed by analytical Hashin-Shtrikman-Willis (HSW) estimates and bounds.