Permeable moving crack in functionally graded piezoelectric strip

Based on the three-dimensional theory of piezoelectric elasticity, the permeable moving crack problem was solved for a functionally graded piezoelectric strip. By using the Fourier transform, the mixed boundary-value problem is first reduced to dual integral equations and then into Fredholm integral equations of the Second kind. The closed forms of the singular stress, strain, electric displacement and electric field are obtained by using asymptotic expansion, and we also got the angular distribution function of the field variables and the intensity factors of relevant quantities near the crack tip. The results obtained for permeable crack show that the field variables near the crack tip in a functionally graded piezoelectric strip all possess the square root singularity, and they are in terms of the local coordinates attached to the moving crack tip; the moving crack has a tendency to turn away from the crack face when the velocity is increased.