Basic solution of four parallel non-symmetric permeable Mode-III cracks in a piezoelectric/piezomagnetic composite plane

Abstract

The interaction of four parallel non-symmetric permeable cracks in a piezoelectric/piezomagnetic composite plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through a Fourier transform into four pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the relationships among the electric displacement, magnetic flux and stress fields near the crack tips were obtained. The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the lengths and spacing of cracks. It was also revealed that the crack shielding effect is present in piezoelectric/piezomagnetic composites.

Keywords:

• piezoelectric/piezomagnetic composite
• non-symmetric cracks
• crack shielding effect
• mechanics of solids

Acknowledgments

This work was supported by the Natural Science Foundation with Excellent Young Investigators of Hei Long Jiang Province(JC04-08) and the National Natural Science Foundation of China (10572043), the Natural Science Foundation of Hei Long Jiang Province(A2007-05).