Equivalent inhomogeneity method for evaluating the effective conductivities of isotropic particulate composites

The problem of calculating the effective conductivity of isotropic composite materials with periodic or random arrangements of spherical particles is revisited by using the equivalent inhomogeneity method. The approach can be viewed as an extension of classical Maxwell's methodology. It is based on the idea that the effective conductivity of the composite material can be deduced from the effect of the cluster embedded in an infinite space on the far-fields. The key point of the approach is to precisely account for the interactions between all the particles in the cluster that represent the composite material in question. It is done by using a complete, multipole-type analytical solution for the problem of an infinite isotropic matrix containing a finite cluster of isotropic spherical particles, regarded as the finite cluster model of particulate composite. The effective conductivity of the composite is evaluated by applying the " singularto-singular" re-expansion formulae and comparing the far-field asymptotic behavior with the equivalent inhomogeneity solution. The model allows one to adequately capture the influence of the micro-structure of composite material on its overall properties. Numerical realization of the method is simple and straightforward. Comparison of the numerical results obtained by the proposed approach with those available in literature (both for periodic and random arrangements) demonstrate its accuracy and numerical efficiency.