Revisiting the generalized self-consistent scheme in composites: Clarification of some aspects and a new formulation

The determination of an effective property in composite materials necessitates the knowledge of some averaged field quantities in the constituents (like the average heat intensity or average strain) of a composite sample, which is subjected to homogeneous boundary conditions. In the generalized self-consistent scheme (GSCS) which is today a classical micromechanics model suited for the determination of the effective properties of matrix-based composites, those average quantities are estimated by using an auxiliary configuration in which a particulate phase is first surrounded by some matrix material and then embedded in the effective medium. In the present study, we revisit the GSCS both for two- and multi-phase matrix-based composites containing spherical particles, and clarify aspects related to the volume fractions of the particle core and matrix shell within the composite element which is embedded in the effective medium. The contribution of this study is believed to be mainly on the conceptual side and resides in a new formulation of the method in which the embedding volume fractions are determined in the course of the analysis by means of some fundamental relations on the averaged fields. The study is carried out in thermal conduction and elasticity and contains new results on the effective shear modulus of multi-phase composites.