Pei-Wei Zhang

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

The solutions to two or four parallel Mode-I permeable cracks in magnetoelectroelastic composite materials are derived using the generalized Almansis 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.

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

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.

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

The non-local theory solution of two collinear mode-I permeable cracks in a magnetoelectroelastic composite material plane was investigated using the generalized Almansis 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.

Multiple parallel symmetric permeable model-III cracks in a piezoelectric/piezomagnetic composite material plane

In this paper, the interactions of multiple parallel symmetric and permeable finite length cracks in a piezoelectric/piezomagnetic material plane subjected to anti-plane shear stress loading are studied by the Schmidt method. The problem is formulated through Fourier transform into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relation between the electric field, the magnetic flux field and the stress field near the crack tips is obtained. The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the length and spacing of the cracks. It is also revealed that the crack shielding effect presents in piezoelectric/piezomagnetic materials.