Abstract
The generalized alternating method of Schwarz was applied to boundary value problems for a multiply connected domain in the prior work Part I [62] . Approximate analytical formulas for the effective properties of dispersed composites with the exactly derived precision of their validity in concentration and in contrast parameter were derived. The present paper is devoted to comparison study of the formulas from Part I and the previously used engineering approximations. It is demonstrated that self-consistent methods (effective medium approximation, mean field, Mori-Tanaka methods etc) can be considered as the first order approximation of Schwarz's method. Implementation of the reiterated homogenization by means of Schwarz's method is also analyzed. This investigation explains a plenty of illusory different formulas which are actually reduced to the same lower order estimations for dilute composites. Some self-consistent methods violate the principles of homogenization and lead to methodologically misleading approaches. • A self-consistent method for composites is reduced to Schwarz's alternating method. • A methodology to study dispersed random composites is developed. • Limitations of various self-consistent methods are analyzed.
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