The energy release rate for a Griffith crack in a piezoelectric material

The plane solution giving the stresses and electric fields in an infinite body around a cylindrical cavity with an elliptical cross-section is presented. The energy change in an infinite body due to the introduction of an elliptical cavity having an electric field within it is calculated. The electric field from the interior of the cavity is then used in conjunction with the energy change formula to calculate the total energy release rate per crack tip when a Griffith crack propagates. Due to a change of stored electrostatic energy within the crack, the total energy release rate is not equal to the energy release rate at the crack tips as the material separates. The implications for fracture and crack growth are discussed.