Fracture analysis of mode III crack problems for the piezoelectric bimorph

In this paper, a symplectic method based on the Hamiltonian system is proposed to analyze the interfacial fracture in the piezoelectric bimorph under anti-plane deformation. A set of Hamiltonian governing equations is derived from the Hamiltonian function by introducing dual variables of generalized displacements and stresses which can be expanded in series in terms of the symplectic eigensolutions. With the aid of the adjoint symplectic orthogonality, coefficients of the series are determined by the boundary conditions along the crack faces and along the external geometry. The stress\electric displacement intensity factors and energy release rates (G) directly relate to the first few terms of the nonzero eigenvalue solutions. The two ideal crack boundary conditions, namely the electrically impermeable and permeable crack assumptions, are considered. Numerical examples including the complex mixed boundary conditions are considered to show fracture behaviors of the interface crack and discuss the influencing factors.