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

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New finite elements with embedded strong discontinuities for the modeling of failure in electromechanical coupled solids (2011, background): “Oneparticular areaof controversyexists when it comes to the choice of appropriate boundary conditions along existing and propagating crack faces [17,23,38,31].”
Energetically consistent boundary conditions for electromechanical fracture (2004, methodology): “These electrical boundary conditions along with traction free mechanical boundary conditions have been investigated by numerous authors including Hao and Shen (1994), Sosa and Khutoryansky (1996), McMeeking (1999), Xu and Rajapakse (2001), Gruebner et al. (2003), and McMeeking (2004) among others.”
Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions (2012, background): “…these models are useful to study the basic concepts of the linear theory in the context of fracture mechanics and to evaluate the effects of individual and coupled electromechanical fields and different crack-face boundary conditions (McMeeking, 1999, 2004; Landis, 2004a; Li et al., 2008).”