An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution

Abstract

For estimating the effective properties (elasticity, conductivity, piezoelectricity, etc.) of composites of the matrix-inclusion type, we develop a new micromechanical model, the effective self-consistent scheme (ESCS), based on the three-phase model. As a simplified and explicit version of the ESCS estimate, the interaction direct derivative (IDD) estimate is further proposed. The IDD estimate has an explicit and almost the simplest structure in comparison with other existing micromechanical estimates, with clear physical significance for all the involved components. It is universally applicable for various multiphase composites of the matrix-inclusion type, for any material symmetries of matrix, inclusions and effective medium, and distribution, shapes, orientations, and concentration of inclusions. Applications to effective elastic properties of composites with spherical inclusions and materials damaged due to voids of various shapes and microcracks (up to any high microcrack density) are presented, in comparison with a number of refined or accurate numerical simulation results. The IDD estimate seems to provide the best predictions in most of our examined cases. A further exploration of the proposed two estimates is given by Du and Zheng (Acta Mech. (2001), in press).