Fracture behaviour of cracks in piezoelectric media with electromechanically coupled boundary conditions

Existing studies on slit crack problems have been limited mostly to the electrically impermeable and permeable crack models, which represent the limiting cases of the physical boundary condition. This paper studies the generalized plane problem of a crack in a piezoelectric medium, with the electric boundary condition along the crack surfaces being governed by its opening displacement. The theoretical formulation of this nonlinear problem is based on the use of Fourier transforms and the solution of a system of integral equations, which are solved using Chebyshev polynomials. The analytical solution of the problem clearly shows the transition between permeable and impermeable models with increasing crack opening. Depending on the applied mechanical and electric loads, different modes of crack deformation are predicted and discussed.