A generalized self‐consistent mori‐tanaka scheme for prediction of the effective elastic moduli of hybrid multiphase particulate composites

Abstract A generalized self‐consistent Mori‐Tanaka method (GSCMTM) is developed in this paper. The method starts with the formulation of the problem of heterogeneous elasticity proposed by Dederichs and Zeller and incorporates the strain equivalence condition of Christensen's generalized self‐consistent method (GSCM) and Hill's interfacial operator theory into the evaluation of the strain concentration tensors of constituents. For a two‐phase composite with spherical inclusions, the effective moduli predicted by GSCMTM coincide with those predicted by the Mori‐Tanaka method (MTM). By a two‐step homogenization technique, GSCMTM was successfully extended to multiphase composites. The effective moduli predicted by GSCMTM for multiphase hybrid particulate composites agree well with the existing theoretical and experimental results and can be expressed in a simple explicit form.