Two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

Zhou, Zhen-Gong; Wang, Biao

doi:10.1016/j.ijsolstr.2004.03.004

Cited by 68 publications

(37 citation statements)

References 24 publications

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“…Since then, most research results published were obtained recently in references [1,[12][13][14][15][16][17][19][20][21][22][23][24]. Recently, the static fracture behaviors of a crack or two cracks in piezoelectric/piezomagnetic materials had been investigated in references [25][26][27][28] by the Schmidt method [29] until recent years, but they just concentrated on the anti-plane shear fracture problems in magnetoelectroelastic composite materials.…”

Section: Introductionmentioning

confidence: 99%

Solutions to a limited-permeable crack or two limited-permeable collinear cracks in piezoelectric/piezomagnetic materials

Zhou

Zhang

2007

Arch Appl Mech

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The solutions of a limited-permeable crack (case I) or two collinear limited-permeable cracks (case II) in piezoelectric/piezomagnetic materials subjected to a uniform tension loading were investigated in this paper using the generalized Almansi's theorem. At the same time, the electric permittivity and the magnetic permeability of air in crack were firstly considered. 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 jumps of displacements across crack surfaces, not the dislocation density functions or the complex variable 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 electric displacement intensity factors, magnetic flux intensity factors and stress intensity factors at crack tips.

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Section: Introductionmentioning

confidence: 99%

Solutions to a limited-permeable crack or two limited-permeable collinear cracks in piezoelectric/piezomagnetic materials

Zhou

Zhang

2007

Arch Appl Mech

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“…As discussed in the works (21), (22), (30) and the above discussion, it can be seen that the Schmidt method performs satisfactorily if the first ten terms of the infinite series in Eq. (43) are retained.…”

Section: Numerical Calculations and Discussionmentioning

confidence: 66%

“…(41) and (42) can be evaluated directly. Equation (38) can now be solved for the coefficients b n by the Schmidt method (21), (22) . For brevity, Eq.…”

Section: Solution Of the Triple Integral Equationsmentioning

confidence: 99%

“…More recently, the concept of functionally graded materials was firstly extended to the piezoelectric/piezomagnetic materials to improve the reliability of piezoelectric/piezomagnetic materials and structures in Ref. (21). The results also showed that the singular stress, the singular electric displacements and the singular magnetic flux in functionally graded piezoelectric/piezomagnetic materials carry the same forms as those in the homogeneous piezoelectric/piezomagnetic materials but the magnitudes of the intensity factors depend significantly upon the gradient of the functionally graded piezoelectric/piezomagnetic materials properties.…”

Section: Introductionmentioning

confidence: 99%

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Two Collinear Interface Cracks between Two Dissimilar Functionally Graded Piezoelectric/Piezomagnetic Material Layers under Anti-Plane Shear Loading

Liang

2006

JSME Int. J., Ser. A

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In this paper, the behavior of two collinear interface cracks between two dissimilar functionally graded piezoelectric/piezomagnetic material layers subjected to an anti-plane shear loading is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with coordinate vertical to the crack. By using the Fourier transform, the problem can be solved with the help of a pair of triple integral equations in which the unknown variable is the jump of the displacement across the crack surfaces. These equations are solved using the Schmidt method. The normalized stress, the electrical displacement and the magnetic flux intensity factors are determined for different geometric for the permeable electric boundary conditions. The relations among the electric filed, the magnetic flux field and the dynamic stress field near the crack tips can be obtained. Numerical examples are provided to show the effect of the functionally graded parameter and the thickness of the strip upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.

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“…Li and Weng [9] first considered the static anti-plane problem of a finite crack in a functionally graded piezoelectric material strip. More recently, Zhou and Wang [11,12] first studied the static ant-plane shear problems of two parallel cracks and a crack in functionally graded piezoelectric/piezomagnetic materials by using Schmidt method [13].…”

Section: Introductionmentioning

confidence: 99%

Basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials

2007

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The basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials was studied in this paper using the generalized Almansi's theorem. To make the analysis tractable, it was assumed that the shear modulus varies exponentially along the horizontal axis parallel to the crack. The problem was formulated through a Fourier transform into two pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surface. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. The solution of the present paper shows that the singular stresses and the singular electric displacements at the crack tips in functionally graded piezoelectric materials carry the same forms as those in homogeneous piezoelectric materials; however, the magnitudes of intensity factors depend on the gradient of functionally graded piezoelectric material properties. It was also revealed that the crack shielding effect is also present in functionally graded piezoelectric materials.

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Two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading

Cited by 68 publications

References 24 publications

Solutions to a limited-permeable crack or two limited-permeable collinear cracks in piezoelectric/piezomagnetic materials

Solutions to a limited-permeable crack or two limited-permeable collinear cracks in piezoelectric/piezomagnetic materials

Two Collinear Interface Cracks between Two Dissimilar Functionally Graded Piezoelectric/Piezomagnetic Material Layers under Anti-Plane Shear Loading

Basic solution of two parallel mode-I permeable cracks in functionally graded piezoelectric materials

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