Micromechanical Analysis for Macroscopic Dielectric Constants of Composite Materials Including Double Inhomogeneous Inclusions

Abstract

In this study, by applying the double inclusion method to thermal and electromagnetic problems, micromechanical modeling and analysis is performed for a composite material containing many double inhomogeneous inclusions. In modeling, the inner and outer shapes of double inhomogeneous inclusions are ellipsoid that are different from each other. The interaction field due to the presence of many double inhomogeneous inclusions is evaluated using the Mori-Tanaka theorem. The macroscopic dielectric constants of the composite material are derived explicitly by terms of the difference in shape between inner region and outer one of a double inhomogeneous inclusion. It is shown that the independent number of macroscopic dielectric constants of the composite material is the same as that of an orthorhombic material. For the special case where the shape of inner region and outer one of a double inhomogeneous inclusion are sphere or fiber, the present results are compared with results of the Hashin and Shtrikman's bounds, the Benveniste and Miloh's solution, the Hatta and Taya's solution and the solution derived by the self-consistent method. Furthermore, calculations were performed for the case where the shape of double inhomogeneous inclusions is confocal spheroid. Based on results of these calculations, the validity of this analytical solution is examined.

Keywords

• micromechanics
• double inclusion method
• inhomogeneous inclusion
• mori-tanaka theorem
• macroscopic dielectric constants