Solutions to two or four parallel Mode-I permeable cracks in magnetoelectroelastic composite materials

Abstract

The solutions to two or four parallel Mode-I permeable cracks in magnetoelectroelastic composite materials are derived using the generalized Almansi's theorem under permeable electric and magnetic boundary conditions. The problem can be solved through the Fourier transform with the help of two pairs of dual integral equations, in which unknown variables were jumps of displacements across crack surfaces, not dislocation density functions. To solve the dual integral equations, the jumps of displacements across crack surfaces were directly expanded in a series of Jacobi polynomials to obtain the relations among the electric displacement intensity factors, the magnetic flux intensity factors and the stress intensity factors at the crack tips. The paper presents the interactions of two or four parallel Mode-I cracks in magnetoelectroelastic composite materials and the crack-shielding effect in magnetoelectroelastic composite materials.

Acknowledgements

We would like to thank the National Natural Science Foundation of China (10572043), the Natural Science Foundation for Excellent Young Researchers of Heilongjiang Province (JC04-08), the National Science Foundation for Excellent Young Researchers of China (10325208) and the National Natural Science Key Item Foundation of China (10432030) for their financial support.