Two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

In this paper, the behavior of two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials subjected to an anti-plane shear loading is investigated. To make the analysis tractable, it is assumed that the material properties c(44), e(15), e(11), q(15), d(11) and mu(11) vary exponentially with coordinate parallel to the crack. By using the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces. These equations are solved using the Schmidt method. The normalized stress, the electrical displacement and the magnetic flux intensity factors are determined for different geometric for the permeable electric boundary conditions. Numerical examples are provided to show the effect of the geometry of the interacting crack and the parameter beta describing the functionally graded materials upon the stress intensity factor of the cracks. (C) 2004 Elsevier Ltd. All rights reserved.