Stiffness of Three-Phase Concentric Composite Solids

There are numerous examples of three-phase concentric composites, including coated fiber-reinforced materials and syntactic foams. The stiffness of such three-phase materials is usually investigated by micromechanical methods specified for this particular case. For example, Luo and Weng presented solutions for three-phase concentric spheres [1] and for three-phase concentric cylinders models [2] of an inclusion, a coating (“intermediate matrix”), and a matrix using the Mori–Tanaka method. Among numerous studies of three-phase or multi-phase composites one can mention [3-6].

The present approach employs a combination of two-phase matrix-inclusion models to determine the stiffness of a three-phase solid. The advantage of the proposed method is its simplicity, i.e. a reduction of the three-phase composite micromechanics to a superposition of available two-phase solutions, without a need in additional analytical procedures. This method is also universal and can be applied with any micromechanical theory available for two-phase composites.

Keywords: Composite materials; Micromechanics; Coated fibers; Syntactic foams