Effective elastic moduli of a particulate composite in terms of the dipole moments and property contribution tensors

The paper focuses on the comparison of two approaches used for calculation of the effective elastic properties of particulate composites: the dipole moments representation and the technique based on property contribution tensors. Its specific goal is to bridge the gap between the two methods and to identify the key microstructural parameters affecting overall elastic stiffness of heterogeneous materials. The basic concepts of the homogenization theory including a consistent way of introducing the macroscopic field parameters are discussed and clarified. We provide a detailed comparison of the analytical expressions for the dipole moment tensors obtained by the multipole expansion method and for the stiffness contribution tensors and show that they coincide.