Non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane

Abstract

The non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane was investigated using the generalized Almansi's theorem and the Schmidt method. The problem was formulated through Fourier transform into two pairs of dual integral equations, in which the unknown variables are the jumps in displacements across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of crack length, the distance between two collinear cracks and the lattice parameter on the stress field, the electric displacement field and the magnetic flux field near the crack tips. Unlike the classical elasticity solutions, it is found that no stress, electric displacement or magnetic flux singularities are present at the crack tips in a magnetoelectroelastic composite material plane. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion.

Keywords:

• magnetoelectroelastic composite materials
• two collinear cracks
• non-local theory
• Schmidt method
• lattice parameter

Acknowledgements

The authors are grateful for financial support by the National Natural Science Foundation of China (10572043, 10872057), the Natural Science Foundation with Excellent Young Investigators of Hei Long Jiang Province (JC04-08), and the Natural Science Foundation of Heilongjiang Province (A2007-05).