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 “singular-to-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.