Analysis for macroscopic physical properties of composite materials containing ellipsoidal reinforcements oriented randomly

Abstract

Christensen derived solutions of macroscopic elastic constants of composite materials containing randomly oriented fibers (Christensen, 2005). In this study, by extending Christensen’s method, the analysis of macroscopic physical properties of a composite material containing ellipsoidal reinforcements oriented randomly will be performed. Macroscopic elastic constants, thermal expansion coefficients and dielectric constants of the composite material could be expressed explicitly by using solutions for ellipsoidal reinforcement oriented unidirectionally. As a result of calculations for various ellipsoidal shapes of reinforcement by using derived solutions, it was confirmed that these analytical results of macroscopic physical properties exist between the upper and lower bounds of Hashin et al. Furthermore, by comparing the present result with the result of solution based on Mori-Tanaka’s theory and the experimental result, the validity and applicable range of the analytical solutions were examined.

Keywords

• elastic constant
• thermal expansion coefficient
• dielectric constant
• ellipsoidal reinforcement
• upper and lower bounds
• mori-tanaka’s theory