Effective Medium Approach to Matrix-Inclusion Type Composite Materials

Abstract

This paper addresses a problem of finding the effective medium that exhibits the same overall response as a given composite material reinfored by unidirectional short-fibers (chopped fibers). The expression for the displacement field in composites is obtained by converting the equilibrium equation into an integro-differential equation using the quasi-static Green’s function for a homogeneous medium. The “effective medium” is chosen that the ensemble averaged displacement field for the composite is equal to that of an equivalent homogenous medium. The “effective stiffness” and the “effective mass density” are defined as those properties of the effective medium. This is a first preliminary attempt to analyze the elasto-dynamic effect of matrix-inclusion type of composites. The obtained result for the effective stiffness is new and is not symmetrical with the interchange of the matrix phase and the fiber phase, unlike previous models. The result is also favorably compared with experimental data for spherical-inclusion reinforced composites.