Bound theorem and implementation of dual finite elements for fracture assessment of piezoelectric materials

Owing to the complexity of piezoelectric crack problems, derivation of closed-form solutions is virtually impossible and numerical solutions are largely resorted to. Hence, the upper and lower bound estimation for piezoelectric fracture parameters are of theoretical and practical values. An alternative assessment approach for electromechanical coupling cracked system is suggested in the paper. The dual path-independent integrals and the related bound theorems are presented. Consequently, the dual piezoelectric finite elements are formulated and implemented in bound analysis.