Accuracy of the replacement relations for materials with non-ellipsoidal inhomogeneities

In this paper, we focus on replacement relation that links the property contribution tensors of inhomogeneities having the same shape but different elastic properties. We check the possibility to apply the relations, originally derived for ellipsoidal inhomogeneities (Sevostianov & Kachanov 2007) to ones of non-ellipsoidal shape. We discuss inhomogeneities of superspherical shape, described by equation x2p + y2p + z2p ≤ 1 and show that the replacement relations can be used in the rank of convex shapes (p > 0.5), while for concave shapes the error is significant. In practical applications, it means that for materials with convex inhomogeneities results obtained for effective elastic constants of a porous material can be used to approximately evaluate effective properties of a composite of the same morphology.