On micromechanics approximation for the effective thermoelastic moduli of multi-phase composite materials

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. (C) 1999 Elsevier Science Ltd. All rights reserved.