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

作者：Zhou Zhen Gong^*; Zhang Pei Wei; Wu Lin Zhi

来源：Philosophical Magazine, 2010, 90(13): 1743-1769.

DOI：10.1080/14786430903473007

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

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.

• 出版日期2010
• 单位哈尔滨工业大学