A unified model for piezocomposites with non-piezoelectric matrix and piezoelectric ellipsoidal inclusions

Abstract

In this paper, the closed-form solutions of the electroelastic Eshelbys tensors of a piezoelectric ellipsoidal inclusion in an infinite non-piezoelectric matrix are obtained via the Greens function technique. Based on the generalized Budianskys energy-equivalence framework and the closed-form solutions of the electroelastic Eshelbys tensors, a unified model for multiphase piezocomposites with the non-piezoelectric matrix and piezoelectric inclusions is set up. The closed-form solutions of the effective electroelastic moduli of piezocomposites are also obtained. The unified model has a rigorous but simple form, which can describe the multiphase piezocomposites with different connectivities, such as 0–3, 1–3, 2–2, 2–3, 3–3 connectivities, etc. It can also describe the effects of non-interaction and interaction among the inclusions. As examples, the closed-form solutions of the effective electroelastic moduli are given by means of the dilute solution for the 0–3 piezocomposite with transversely isotropic piezoelectric spherical inclusions and by means of the dilute solution and the Mori–Tanakas method for the 1–3 piezocomposite with two kinds of transversely isotropic piezoelectric cylindrical inclusions. The predicted results are compared with experimental data, which shows that the theoretical curves calculated by means of the Mori–Tanakas method agree quite well with the experimental values, but the theoretical curves obtained by the dilute solution agree well with the experimental values only when the volume fraction of the ceramic inclusion is less than 0.3. The results in this paper can be used to analyze and design the multiphase piezocomposites.