Dipole moments, property contribution tensors and effective conductivity of anisotropic particulate composites

The paper addresses the homogenization problem for a particulate composite with anisotropic constituents. Its specific goal is to bridge the gap between two different approaches to the problem of homogenization focusing on the anisotropic materials and to identify and discuss the key microstructural parameters affecting overall conductivity of heterogeneous materials. The basic concepts of the homogenization theory including a consistent way of introducing the macroscopic field parameters are discussed and clarified. The exact explicit relations have been obtained between the dipole moments, property contribution tensors and effective conductivity of composite with phase anisotropy of the general type. A detailed comparison of the analytical expressions for the dipole moments obtained by the multipole expansion method and the independently derived expressions for the conductivity contribution tensors has been made between and their equivalence is shown for the matrix type composites with transversely isotropic constituents and spheroidal inhomogeneities. The numerical examples illustrate effect on the overall conductivity of particulate composite of the properties of constituents, shape, volume content, spatial arrangement and orientation of particles.