Composites with periodic microstructure

Abstract

For an elastic body containing periodically distributed inhomogeneities, a general procedure is developed for estimating the overall properties of the composite in terms of several infinite series which, for the isotropic matrix (but anisotropic inclusions), depend only on the geometry of the inhomogeneities and hence can be calculated once and for all for each geometry. These infinite series are obtained and tabulated for ellipsoidal inhomogeneities, and the results are used to estimate the overall elastic moduli of composites which contain spherical or ellipsoidal voids or elastic inclusions.