Effective Medium of Unidirectional Short-Fiber Composites by a Self-Consistent Method

Abstract

A new self-consistent method is proposed to calculate the effective stiffness of unidirectional short-fiber composites where each transversely-isotropic short-fibers is embedded in an infinite homogeneous matrix phase. The equilibrium equation for the elastic field in short-fiber composite materials is converted into an integro-differential equation using the Green’s function for a homogeneous medium. The “effective medium” is chosen in such a way that the ensemble averaged strain field for the composite is equal to that of the homogeneous medium that exhibits the same overall response as the composite. The “effective stiffness” and the “effective mass density” are defined as those properties of the effective medium. The obtained expression for the effective stiffness is new and is not symmetrical with the matrix phase and the fiber phase, thus, reflecting the matrix role more properly than previous works which gave symmetrical results. The result is also favorably compared with experimental data.