Overall behavior of composites with periodic multi-inhomogeneities

When applying the equivalent inclusion method (EIM) to a composite material with non-dilute distribution of reinforcement particles, due to the complex interaction between the particles, the homogenizing eigenstrain field will in general be highly nonlinear. The interaction becomes more complex, when the reinforcements are multi-phase particles, i.e., the core inhomogeneity is surrounded by many layers of coatings. In this paper, a treatment for an accurate determination of the distribution of homogenizing eigenstrain fields corresponding to composites with non-dilute periodic distribution of multi-phase reinforcement particles is given. The proposed method is applicable to problems, where the reinforcement particles have: very thick coatings; functionally graded (FG) coatings; or coatings with variable thicknesses. Strong dependence of the overall response of composites on the microstructure of their reinforcement particles is well recognized. The theory is extended to estimate the effective elastic moduli of such composites.