Fundamental electro-elastic field in an infinite transversely isotropic piezoelectric medium with a permeable external circular crack

Abstract

For the first time, exact and fundamental solutions are developed for an infinite transversely isotropic piezoelectric medium, weakened by a circular external crack. The crack is assumed to be electrically permeable and is subjected to mechanical loadings applied symmetrically with respect to the crack face. The problem is transformed into a mixed boundary value problem, which is solved by the generalized potential theory method along with the general piezoelectricity solutions. Three-dimensional non-axisymmetric electro-elastic field is completely and explicitly presented in terms of elementary functions. Singular behaviors on the crack tip and the crack face displacement are examined. For a specific piezoelectric material, numerical calculations are performed to confirm the validity of the present solutions, and to show the electromechanical coupling effect and the influence of electric boundary conditions. The present solutions can serve as benchmarks to clarify various simplified analyses and numerical simulations.