Interacting ellipsoidal inhomogeneities by multipole expansion method and effective conductivity of particulate composite

The complete series solution has been obtained for the potential field of an array of ellipsoidal inhomogeneities regarded as a multi particle model of composite. By combining the superposition principle, the perturbation field expansion in terms of ellipsoidal harmonics and the re-expansion formulas for them, the model boundary value problem is reduced to a set of linear algebraic equations. The obtained solution has been implemented in the modified Maxwell and Ralyeigh homogenization schemes for effective conductivity of ellipsoidal particle composite with an adequate account for the interaction effects. The results of numerical study are provided which illustrate the convergence rate of solution and accuracy of the developed method.