Piezoelectric-conductor iterative method for analysis of cracks in piezoelectric semiconductors via the finite element method

Based on the special coupling properties of the governing equation, constitutive equation, and boundary conditions, the piezoelectric-conductor iterative method is proposed for structural analysis of piezoelectric semiconductors with combined mechanical loading, electric strength field (or electric displacement), and electric current (or electric carrier density). In this approach, the analysis methods for piezoelectric media and conductors, which have been studied intensively and extensively, are used iteratively. In this paper, the piezoelectric-conductor iterative method is first presented and implemented via the finite element method to analyze a cracked piezoelectric semiconductor plate. The extended intensity factors, including the stress intensity factor, the electric displacement intensity factor, and the electric current factor at the crack tip, are calculated. The effects of the applied loadings and geometric sizes on the fracture behaviors of piezoelectric semiconductors are studied.