A Layered-Shell Model of Anisotropic Composites: Extension of the Milgrom and Shtrikman Model

In this work, the extension of the Milgrom and Shtrikman model to anisotropic composite materials containing n-layered hollow ellipsoidal inclusions, is presented. The effective properties of such materials are determined using the Green function techniques and interfacial operators. Here, the basic unit of the microstructure is a hollow system of contacting concentric ellipsoidal shells, each of which is made of one of the components. Space is packed with such units of different sizes, but the same proportions; the cavity within each such shell system is then packed with similar systems and this continues in an infinite nesting sequence. In the final configuration, the effective properties are inside and outside the basic unit of layered shells (n+1). For n=2 and in the case of isotropic material, it is shown that the effective compressibility covers all ranges of the Hashin-Strikman bounds.