Numerical solutions on fracture of piezoelectric materials by hybrid element

Abstract

The cracked piezoelectric problem is observed numerically. To simulate the characteristic singularity at the crack tip, a plane piezoelectric hybrid element is derived. The new model involves displacement u, stress σo, electric displacement D and electric potential p as independent variables. The electromechanical coupling behavior of the cracked piezoelectric ceramics PZT-4 and PZT-5 is investigated. Under impermeable crack condition, the 1/√r-singularity at the crack-tip zone is exactly represented for σ and D. The efficiency of implementing the permeable crack condition is also inspected. To examine current energy release rate formulas, the path-independent integral is computed, and then a fitting formula for the energy release rate is obtained. In this paper, all the numerical results are compared with the previously reported theoretical solutions. © 2001 Elsevier Science Ltd. All rights reserved.