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EFFECTIVE PROPERTIES OF DISCRETE RANDOM COMPOSITES WHEREIN THE HOST AND INCLUSION PHASES OBEY DIFFERENT CONSTITUTIVE RELATIONS V V. Varadan, R. T. Apparao and V. K. Varadan Research Center for the Engineering of Electronic and Acoustic Materials Department of Engineering Science and Mechanics The Pennsylvania State University University Park, PA - 16802

ABSTRACT In studying the effective medium theories, polarization is hardly given a consideration in deciding the effective properties of a composite where the host and inclusion phases follow different constitutive equations. A significant conclusion of this paper is that eventhough the composite has discrete inclusions, with the inclusion phase obeying different constitutive properties than the host, the effective medium shows a preference for the inclusion behavior rather than the host which is continuous. As an example, results on polarization study are detailed for the specific case of chiral composites. Application of similar principles is presently explored in more complex problems like the elastic wave propagation through piezoelectric composites and the acoustic wave propagation through sediments.

INTRODUCTION A composite material is an inhomogeneous medium where the scale of inhomogeneities can range from the nano to the macroscale. If the inhomogeneous regions are sufficiently large and uniform, the properties are equal to the bulk properties of one of the components. The composite as a whole can be described by a set of effective bulk properties, as though, it were a statistically homogeneous medium at the length scales of interest. A central problem in the theory of composites is the calculation of such bulk properties. The main difficulty arises when the bulk property of the composite depends on the detailed microgeometry of the composite and the constitutive relations. A random composite material consists of a random network of two or more constituent phases. If the phases form interpenetrating networks, the description of the composite material behavior is quite different from the case when the composite consists of a random distribution of discrete inclusions of one or more phases in a three-dimensionally connected host phase. In the former case, the microstructure or geometry of the constituent phases is not defined and hence cannot enter as a parameter in determining the effective medium behavior. This type of problem has been considered by : Biot[1] in the description of fluid saturated porous solids, by Bruggeman[2] and others. The striking feature of these models is that all of the constituents are treated on an equal basis. In the case of discrete random composites, the microstructure of the inclusion phase, its orientation and distribution in the host phase has to be modeled in sufficient detail depending on the wavelengths of interest. This is best accomplished using a multiple scattering theory (MST) wherein the geometry of the inclusion can be incorporated into the derivation of the scattering matrix or the T-matrix of the inclusion. In t