Investigation of a Griffith crack subject to anti-plane shear by using the non-local theory

Zhou, Zhen-Gong; Han, Jiecai; Du, Shiyu

doi:10.1016/s0020-7683(98)00179-6

Cited by 77 publications

(35 citation statements)

References 6 publications

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“…(31) can be easily evaluated numerically. Equation (31) can now be solved for the coefficients b n by the Schmidt method [18][19][20]. For brevity, Eq.…”

Section: Solution Of the Dual Integral Equationsmentioning

confidence: 99%

“…However, relatively few works on the crack problem in functionally graded piezoelectric/piezomagnetic materials have been carried out. To our knowledge, the electro-elastic behavior of functionally graded piezoelectric/piezomagnetic materials with a crack subjected to an anti-plane shear loading has not been studied by using the Schmidt method [18][19][20]. Thus, the present work is an attempt to fill this requirement.…”

Section: Introductionmentioning

confidence: 99%

“…The magneto-electro-elastic behavior of a crack in functionally graded piezoelectric/piezomagnetic materials subjected to an anti-plane shear stress loading is investigated using the Schmidt method [18][19][20]. The Fourier transform is applied and a mixed boundary-value problem is reduced to a pair of dual integral equations.…”

Section: Introductionmentioning

confidence: 99%

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The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

Zhou

Wang

2005

Archive of Applied Mechanics

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In this paper, the behavior of a crack in functionally graded piezoelectric/piezomagnetic materials subjected to an anti-plane shear loading is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using a Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. These equations are solved using the Schmidt method. The relations among the electric displacement, the magnetic flux and the stress field near the crack tips are obtained. Numerical examples are provided to show the effect of the functionally graded parameter on the stress intensity factors of the crack.

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“…(31) can be easily evaluated numerically. Equation (31) can now be solved for the coefficients b n by the Schmidt method [18][19][20]. For brevity, Eq.…”

Section: Solution Of the Dual Integral Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

Zhou

Wang

2005

Archive of Applied Mechanics

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“…(24) and (25) with four unknown functions, substituting the solutions into Eq. (19) and applying the boundary conditions, it can be obtained…”

Section: Solutionmentioning

confidence: 99%

Investigation of the Behavior of an Interface Crack between Two Half-Planes of Orthotropic Functionally GradedMaterials by Using a New Method

Zhou

Wang

Yang

2004

JSME Int. J., Ser. A

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In this paper, the problem of a crack along an interface between inhomogeneous orthotropic media is solved by using a new method, named the Schmidt method. To make the analysis tractable, it is assumed that the Poisson's ratios of the mediums are constant and the material modulus varies exponentially with coordinate parallel to the crack. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the length of the crack and the parameter describing the functionally graded materials upon the stress intensity factor of the cracks. When the material properties are continuous across the crack line, the numerical results are the same as those obtained so far. When the material properties are not continuous across the crack line, an approximate solution of the interface crack problem is given under the assumptions that the effect of the crack surface overlapping very near the crack tips is negligible. Contrary to the previous solution of the interface crack, it is found that the stress singularities of the present interface crack solution are similar with ones for the ordinary crack in homogenous orthotropic materials.

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“…This can be used to predict the cohesive stress for various materials and the results close to those obtained in atomic lattice dynamics (27), (28) . Recently, some static and dynamic fracture problems (29) - (35) in an isotropic elastic material, the functionally graded materials and the piezoelectric material have been studied by use of the non-local theory. The traditional concept of linear elastic fracture mechanics and the non-local theory are extended to include the piezoelectric effects and the functionally graded materials.…”

Section: Introductionmentioning

confidence: 99%

Investigation the Dynamic Interaction between Two Collinear Cracks in the Functionally Graded Piezoelectric Materials Subjected to the Harmonic Anti-Plane Shear Stress Waves by Using the Non-Local Theory

Liang

2006

JSME Int. J., Ser. A

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In this paper, the non-local theory of elasticity is applied to obtain the dynamic interaction between two collinear cracks in functionally graded piezoelectric materials under the harmonic anti-plane shear stress waves for the permeable electric boundary conditions. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the crack. By means of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations that the unknown variable is the jump of the displacement across the crack surfaces. These equations are solved by use of the Schmidt method. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips. The non-local elastic solutions yield a finite stress at the crack tips, thus allows us to use the maximum stress as a fracture criterion. The finite stresses at the crack tips depend on the crack length, the distance between two cracks, the functionally graded parameter, the circular frequency of the incident waves and the lattice parameter of the materials, respectively.

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Investigation of a Griffith crack subject to anti-plane shear by using the non-local theory

Cited by 77 publications

References 6 publications

The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

Investigation of the Behavior of an Interface Crack between Two Half-Planes of Orthotropic Functionally GradedMaterials by Using a New Method

Investigation the Dynamic Interaction between Two Collinear Cracks in the Functionally Graded Piezoelectric Materials Subjected to the Harmonic Anti-Plane Shear Stress Waves by Using the Non-Local Theory

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