Several variations of the generalized self-consistent method for hybrid composites

Several medels are proposed to extend the generalized self-consistent method to hybrid composites, i.e. composites with three or more phases. These models degrade to the eigensolution approach in the generalized self-consistent method for two-phased composites. It is established that the difference in elastic moduli predicted by these models, the Mori-Tanaka method and the decoupled model, are small, and all are in reasonable agreement with available experimental data. A solid containing two extreme types of inclusions, voids and rigid particles, is also studied. For the same volume fraction of spherical voids and rigid particles, all models reveal that the weakening effect of voids and the strengthening effect of rigid particles cancel each other out so that the effective Young's modulus of the composite is almost identical to that of the matrix. Among these models, Mori-Tanaka's method and the decoupled model provide closed-form solutions. For a solid with two types of reinfircements, Mori-Tanaka's method gives the lower bounds, and the decoupled method the average estimate for the moduli.