“…The paper of Kuna (2010), Zhang and Gao (2004) and Zhang et al (2002) provided extensive reviewing for the current state of the fracture mechanics research of piezoelectric materials. Recently, the delayed fracture and localized polarization switching near a crack tip in three-point bending piezoceramics under electromechanical loading was discussed (Narita et al 2010), a partition of unity-based cohesive zone finite element model was employed to mimic crack nucleation and propagation in a piezoelectric continuum (Verhoosel et al 2010), and the influences of magnetostriction, electrostriction and piezomagnetic/piezoelectric stiffening on the fracture behavior of a layered multiferroic composite were studied (Li et al 2011). In particular, the penny-shaped crack in piezoelectric materials subjected to electromechanical loading has been received much attention, and several solutions were derived independently (Chen and Shioya 1999;Kogan et al 1996;Shang et al 1996;Wang 1994).…”