The Stress Field in the Vicinity of Two Parallel Symmetric Cracks Subjected to Antiplane Shear Loading in Functionally Graded PiezoelectricPiezomagnetic Materials

In this paper, the problem of two parallel symmetry permeable cracks in functionally graded piezoelectricpiezomagnetic materials subjected to an antiplane shear loading is investigated by use the Schmidt method. To make the analysis tractable, it is assumed that the material properties varied exponentially with coordinate vertical to the crack. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables were the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effect of the geometry of the interacting crack and the functionally graded parameter upon the stress intensity factors. The relations among the electric filed, the magnetic flux field and the stress field are obtained. The shielding effect of two parallel cracks has been discussed.