Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites

Abstract The dilute, self-consistent, Mori-Tanaka and differential micromechanics theories are extended to consider the coupled electroelastic behavior of piezoelectric composite materials. The application of each theory is based on Deeg's (1980, unpublished) rigorous three-dimensional electroelastic solution of an ellipsoidal inclusion in an infinite piezoelectric medium. Each micro-mechanics theory is implemented through a matrix formulation in which the effective electroelastic moduli are conveniently represented by a 9 × 9 matrix. As in the corresponding uncoupled elastic and electric behavior, the dilute and Mori-Tanaka schemes return explicit estimates for the effective electroelastic moduli. The self consistent method, however, returns an implicit nonlinear algebraic matrix equation for the effective electroelastic moduli. The differential scheme formally results in a set of 81 coupled nonlinear ordinary differential equations for the effective electroelastic moduli. In general, recourse to a numerical scheme is required for the self-consistent and differential theories. Numerical results are presented to illustrate the performance of each model for some typical composite microstructures and the models are compared in light of existing experimental data.

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