Simulation of the dielectric constant of a composite material

We evaluate the effective dielectric constant of a composite material consisting of nonoverlapping spherical inclusions of dielectric constant ${\mathrm{\epsilon }}_1$ embedded in a matrix of dielectric constant ${\mathrm{\epsilon }}_2$, by use of an analytic-simulation method. The method proceeds by expanding the polarization of one inclusion in a multipole series and connecting it to the corresponding expansions about the other inclusions. For a given inclusion geometry, these linear equations are solved by matrix algebra. Then, an average over the desired statistical distribution of the inclusions is carried out. We have obtained converged results up to a volume fraction of 0.45 for the most difficult case of conducting inclusions in an insulating matrix. For insulating inclusions in a conducting matrix, we obtain converged results even close to the hexagonal-close-packed volume fraction of 0.74. We also simulate composites consisting of inclusions which are themselves composites.