A generalized self-consistent method for piezoelectric fiber reinforced composites under antiplane shear

Abstract

A three-phase piezoelectric confocal elliptical cylinder model is proposed, and an exact solution is obtained for the model subjected to antiplane mechanical and inplane electrical loads at infinity by using the conformal mapping integrated with the Laurent series expansion technique. Based on the model and solution, a generalized self-consistent method is developed for predicting the relevant effective electroelastic moduli of piezoelectric fiber reinforced composite, accounting for variations in fiber section shapes and randomness in distribution and orientation. The dilute, self-consistent, differential and Mori–Tanaka micromechanics theories for piezoelectric fiber reinforced composites are also extended to consider randomness in fiber section orientation in a statistical sense. A full comparison is made among these five micromechanics methods and with the Hori and Nemat-Nasser's rigorous upper and lower bounds, which shows that the generalized self-consistent method and Mori–Tanaka method can verify each other's results, whereas other micromechanics methods may lead to significant deviations, or even unacceptable results. Finally, as an application of the proposed generalized self-consistent method, the complex factors that influence the effective piezoelectric modulus are discussed.