Abstract
It has been shown that for multi-phase composite materials, the Mori–Tanaka and self-consistent approaches may give non-symmetric effective moduli, may violate some exact connections between the effective moduli, may violate the Hashin–Shtrikman variational bounds, and may exhibit incorrect behavior at the unitary (100%) reinforcement concentration limit. An effective-medium-field micromechanics approximation using normalized concentration factors is proposed and is shown to overcome these difficulties. Such a normalization is necessary to satisfy the consistency relationship.
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