On some controversial issues in effective field approaches to the problem of the overall elastic properties

Several versions of the effective field method of finding the overall elastic properties of matrix composites are examined and compared. We focus on difficulties and uncertainties encountered by these methods, in particular in cases of anisotropic multiphase composites. It is demonstrated that the schemes are best formulated in terms of the compliance/stiffness contributions tensors: such formulation exposes roots of various inconsistencies, and clarifies relations between different versions of the method. Particular attention is paid to Maxwell's scheme which is shown to represent yet another version of the effective field method. The discussion can be extended to physical properties other than the elastic ones. (C) 2013 Elsevier Ltd. All rights reserved.