Wu Linzhi

The scattering of harmonic elastic anti-plane shear waves by two collinear cracks in the piezoelectric plate by using the non-local theory

In this paper, the dynamic interaction between two collinear cracks in a piezoelectric material plate under anti-plane shear waves is investigated by using the non-local theory for impermeable crack surface conditions. By using the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations. These equations are solved using the Schmidt method. This method is more reasonable and more appropriate. Unlike the classical elasticity solution, it is found that no stress and electric displacement singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis.

The elastic field induced by a hemispherical inclusion in the half-space

The elastic field induced by a hekispherical inclusion with uniform eigenstrains in a semi-infinite elastic medium is solved by using the Greens function method and series expansion technique. The exact solutions are presented for the displacement and stress fields which can be expressed by complete elliptic integrals of the first, second, and third kinds and hypergeometric functions. The present method can be used to determine the corresponding elastic fields when the shape of the inclusion is a spherical crown or a spherical segment. Finally, numerical results are given for the displacement and stress fields along the axis of symmetry (x3-axis).

The non-local theory solution of a Griffith crack in functionally graded materials subjected to the harmonic anti-plane shear waves

In this paper, the dynamic stress field near crack tips in the functionally graded materials subjected to the harmonic anti-plane shear stress waves was investigated by means of the non-local theory. The traditional concepts of the non-local theory were extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it was assumed that the material properties vary exponentially with coordinate parallel to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. The magnitude of the finite dynamic stress field depends on the crack length, the parameter describing the functionally graded materials, the circular frequency of the incident waves and the lattice parameter of materials.

THE ELECTRO-ELASTIC FIELD OF THE INFINITE PIEZOELECTRIC MEDIUM WITH TWO PIEZOELECTRIC CIRCULAR CYLINDRICAL INCLUSIONS*

The electro-elastic field of the infinite piezoelectric medium with two piezoelectric circular cylindrical inclusions is derived under the antiplane shear stresses and inplane electric fields. The analytical solution is obtained. The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation. From the results obtained, it can be found that the electro-elastic field depends on the material constants of individual phases, the geometric parameters of the system and the applied antiplane shear stresses and electric fields at infinity. In addition, the specific cases when two circular cylindrical inclusions are tangent to each other and they are holes and/or rigid ones, are also studied in this paper.

A rigid line in a confocal elliptic inhomogeneity embedded in an infinite medium under antiplane shear

An effective method is developed and used to investigate the antiplane problem of a rigid line in a confocal elliptic inhomogeneity embedded in an infinite medium. The analytical solution is obtained. The proposed method is based upon the use of conformal mapping and the theorem of analytic continuation. Special solutions which are verified by comparison with existing ones are provided. Finally, the characteristics of stress singularity at the tip of the rigid line inhomogeneity are analyzed and the extension forces for the crack and the rigid line inhomogeneity are derived.

THE STRESS FIELD IN THE VICINITY OF TWO PARALLEL SYMMETRIC CRACKS SUBJECTED TO ANTI-PLANE SHEAR LOADING IN FUNCTIONALLY GRADED PIEZOELECTRIC/PIEZOMAGNETIC MATERIALS

In this paper, the problem of two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials subjected to an anti‐plane shear loading is investigated by use the Schmidt method. To make the analysis tractable, it is assumed that the material properties varied exponentially with coordinate vertical to the crack. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables were the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces were expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effect of the geometry of the interacting crack and the functionally graded parameter upon the stress intensity factors. The relations among the electric filed, the magnetic flux field and the stress field are obtained. The shielding effect of two parallel cracks has been discussed.

EFFECTIVE ELASTIC MODULI OF AN INHOMOGENEOUS MEDIUM WITH CRACKS

In the present paper, the effective elastic moduli of an inhomogeneous medium with cracks are derived and obtained by taking into account its microstructural properties which involve the shape, size and distribution of cracks and the interaction between cracks. Numerical results for the periodic microstructure of different dimensions are presented. From the results obtained, it can be found that the distribution of cracks has a significant effect on the effective elastic moduli of the material.

A transverse crack tip field in bimaterial

The asymptotic field near an interface crack tip is analyzed with the fully nonlinear theory. By dividing the crack tip field into narrowing sectors and an expanding sector, the asymptotic equations for the crack tip field are derived and solved. The singular characters of stress and strain near the crack tip are revealed.The asymptotic field near an interface crack tip is analyzed with the fully nonlinear theory. By dividing the crack tip field into narrowing sectors and an expanding sector, the asymptotic equations for the crack tip field axe derived and solved. The singular characters of stress and strain near the crack tip are revealed.