Electro-mechanical crack systems: bound theorems, dual finite elements and error estimation

Because of the complexity of piezoelectric crack problems, it is hard to obtain closed-form solutions, and numerical methods are largely resorted to. Hence, the upper/lower bound estimation of piezoelectric fracture parameters is of theoretical and practical importance. in this paper, the path-independent integral I, which is the dual of the J-integral, for electro-mechanical coupling crack systems, is presented. The related bound theorems are established for J and I. Piezoelectric dual finite elements are presented for the numerical implementation of the bound analysis. Moreover, an error estimator is presented for the assessment of numerical accuracy of the piezoelectric fracture parameters.