Self-Consistent Approximations in the Theory of Composites and Their Limitations

Many attempts were undertaken to modify Maxwell’s approach in the theory of composites. Self-consistent methods (effective medium approximation, mean field, Mori-Tanaka methods, reiterated homogenization etc) were advanced to determine the effective properties of composites. It is demonstrated by an example that these extensions are methodologically misleading. They lead to a plenty of illusory different formulas reduced to the Maxwell type, lower order estimation for dilute composites.