Micromechanical Analysis for Macroscopic Elastic Constants and Thermal Expansion Coefficients of Composite Materials Including Double Inhomogeneous Inclusions (1st Report, Derivation of Solutions for Spheroidal Shapes)

Abstract

In this study, micromechanical modeling and analysis is performed for a composite material containing many double inhomogeneous inclusions which consist of a nested sequence of two inhomogeneous inclusions, whose shapes are spheroids that are different from each other. Applying double inclusion method and Mori-Tanaka theorem to this composite material, macroscopic elastic constants and thermal expansion coefficients of the material are formulated 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 elastic constants of the composite material is the same as that of a hexagonal material. It is also examined the solution of macroscopic elastic constants for the special case where the shape of inner region and outer one of a double inhomogeneous inclusion are similar and coaxial. Furthermore, it is confirmed that the independent number of macroscopic elastic constants and thermal expansion coefficients is the same as that of an isotropic material, when shapes of two region of a double inhomogeneous inclusion are spherical.

Keywords

• micromechanics
• double inclusion method
• inhomogeneous inclusion
• mori-tanaka theorem
• macroscopic elastic constants
• macroscopic thermal expansion coefficients