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

•Several versions of the effective field method are expressed in terms of compliance contribution tensors.•Maxwell scheme is shown to be also a variant of effective field method.•Situations when effective field schemes lead to inconsistencies are identified.•Possible approaches to avoid these controversial issues are suggested.

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.