An energetically consistent annular crack in a piezoelectric medium

The analytical treatment of an energetically consistent annular crack in a piezoelectric solid subjected to remote opening electromechanical loading is addressed. Potential functions and Hankel transform in combination with a robust technique are employed to reduce the solution of the mixed boundary value problem into a Fredholm integral equation of the second kind. The limiting case of a penny-shaped crack in a piezoelectric medium with energetically consistent boundary conditions over the crack faces is extracted for the first time. The electrical discharge phenomenon within the crack gap is modeled utilizing a non-linear constitutive law and the effects of the breakdown field on the energy release rate are delineated. The energy release rate, the electric displacement inside the crack gap, and the closing traction on crack faces are plotted for all possible geometries of a non-discharging annular crack.