Abstract
In this paper, a generalized self-consistent method is proposed to predict the effective moduli of a material containing single-phase and randomly oriented spheroidal inclusions, with same aspect ratios. This is achieved by using an energy equivalence framework, associated with a generalization of the classical three phase model to spheroidal inclusions. The localization problem (spheroidal duplex inclusion problem) is formulated with the Papkovitch-Neuber approach; this requires expansion formulae for the spheroidal potentials, which are derived in the Appendix. Finally, the determination of the effective moduli is equivalent to solving a system of nonlinear equations. Effective moduli are presented for various types of inclusions, and comparisons are made with the estimations obtained from the self-consistent and Mori-Tanaka methods. Moreover, the effects of inclusion geometry and spatial distribution of inclusions on the effective moduli are investigated and compared to each other.
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