Maxwell homogenization scheme as a rigorous method of micromechanics: Application to effective conductivity of a composite with spheroidal particles

Maxwell's homogenization scheme (MHS) is formulated in terms of the dipole moments and property contribution tensors of the representative volume element (RVE) of actual composite and of the equivalent inclusion. Provided interactions between the inclusions taken into account, this scheme is rigorous in the sense that the effective properties converge to their exact values with increasing RVE size. To demonstrate its potential, the conductivity problem for a composite with aligned spheroidal inclusions is considered. The convergence of the solution is explored and an effect of structural parameters on the effective conductivity of the composite has been evaluated. The methodological issues of MHS application are discussed including an appropriate shape of the composite RVE and of the equivalent inclusion. It is shown that intelligent (accounting for microstructure of composite) shape choice accelerates convergence of the solution. Practical importance of the developed approach consists in its direct applicability to the images of microstructure obtained by the experimental methods. This makes MHS a convenient tool for estimating effective properties of composites from the observed fragments of microstructure.