A generalized self-consistent mechanics method for composite materials with multiphase inclusions

A generalized self-consistent method (GSCM) based on energy equivalence and an inclusion matrix-composite model is proposed that has applicability to composites with three or more phases. For a solid containing single-phase reinforcements, the present approach is equivalent to the inclusion-matrix-composite model. Both particulate-reinforced and unidirectional fiber-reinforced composites are investigated. For a multiphase composite with a phase volume fraction of c₁,c₂,c₃, ..., it is found that the effective moduli are approximately decoupled such that Ē(c₁,c₂,c₃, ...) / E = Ē₀(c₁)/E × Ē₀c₂/E × Ē₀(c₃/E × ..., where Ē₀(·) is the closed-form effective moduli of the correspondin composites with single-phase reinforcements, and E is the moduli of the matrix material. Compared with experimental data and results from numerical studies, the current approach provides reasonably accurate predictions for the effective moduli of multiphase composites.