Micromechanical Analysis for Macroscopic Elastic Constants and Thermal Expansion Coefficients of Composite Materials Including Double Inhomogeneous Inclusions (2nd Report, Numerical Calculation of Macroscopic Elastic Constants)

Abstract

In the previous study, solutions of macroscopic elastic constants and thermal expansion coefficients for a composite material containing many spheroidal double inhomogeneous inclusions were formulated explicitly by using double inclusion method and Mori-Tanaka theorem. The purpose of this study is to verify the validity of the solutions of macroscopic elastic constants derived in the previous analysis. First, by homogenizing the elastic constants inside the double inhomogeneous inclusions, continuity to the solution for the single inhomogeneous inclusion is confirmed. Secondly, for the cases where shapes of the inner and outer regions of the double inhomogeneous inclusions are both sphere and fiber, analytical results of macroscopic elastic constants are compared with analytical solutions obtained by other research groups, and the accuracy of this analytical solution is examined. Furthermore, the usefulness of this analytical solution is also investigated by calculating the macroscopic elastic constants in the case that shapes of the inner and the outer regions of the double inhomogeneous inclusions are not similar.

Keywords

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