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

Zhou, Zhen-Gong; Zhang, Peiwei; Wu, Linzhi

doi:10.1007/s00419-007-0135-z

Cited by 28 publications

(16 citation statements)

References 40 publications

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“…The geometry of two collinear cracks does not change D c 0 and B c 0 , which is in agreement with the observations given by Zhou et al (2007) for two collinear cracks in a magnetoelectroelastic material and Hao (2001) for multiple collinear cracks in a piezoelectric solid.…”

Section: Inner Crack Tipsupporting

confidence: 90%

Transient response of a magnetoelectroelastic solid with two collinear dielectric cracks under impacts

Zhong

Liu

2009

International Journal of Solids and Structures

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a b s t r a c tDynamic analysis of two collinear electro-magnetically dielectric cracks in a piezoelectromagnetic material is made under in-plane magneto-electro-mechanical impacts. Generalized semi-permeable crackface boundary conditions are proposed to simulate realistic opening cracks with dielectric. Ideal boundary conditions of a combination of electrically permeable or impermeable and magnetically permeable or impermeable assumptions are several limiting cases of the semi-permeable dielectric crack. Utilizing the Laplace and Fourier transforms, the mixed initial-boundary-value problem is reduced to solving singular integral equations with Cauchy kernel. Dynamic intensity factors of stress, electric displacement, magnetic induction and crack opening displacement (COD) near the inner and outer crack tips are determined in the Laplace transform domain. Numerical results for a special magnetoelectroelastic solid are calculated to show the influences of the dielectric permittivity and magnetic permeability inside the cracks on the crack-face electric displacement and magnetic induction. By means of a numerical inversion of the Laplace transform, the variations of the normalized intensity factors of stress and COD are discussed against applied magnetoelectric impact loadings and the geometry of the cracks for fully impermeable, vacuum, fully permeable cracks and shown in graphics.

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Section: Inner Crack Tipsupporting

confidence: 90%

Transient response of a magnetoelectroelastic solid with two collinear dielectric cracks under impacts

Zhong

Liu

2009

International Journal of Solids and Structures

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“…2 to (I) According to Eqs. (24)-(32), the stress intensity factors, the electric intensity factors and the magnetic flux intensity factors possess of the same changing rule and only different in magnitudes coming from 0 h , 70 h and 80 h , which had been discussed in references [9,17] . So during the following discussion, the electric displacement intensity factors and the magnetic flux intensity factors would not be elaborated particularly for the simplicity of the article, except the generalized intensity factors show a different variation.…”

Section: Numerical Results and Discussionmentioning

confidence: 94%

“…The limited-permeable crack model, developed in Zhong's [10] and Zhou's [9,11] works, is adopted here. The boundary conditions on crack-surfaces and at infinity for 3D problem are expressed in detail as follows: (1) (2) 0…”

Section: Limited-permeable Boundary Conditionsmentioning

confidence: 99%

“…As discussed in previous work [7] , the boundary condition on the crack surface was complex in piezoelectric/piezomagnetic composites. The limited-permeable boundary condition first proposed in Hao's work [8] for piezoelectric materials was developed into magneto-electro-elastic composites by Zhong et al [5] and Zhou et al [9] , respectively.…”

Section: Introductiomentioning

confidence: 99%

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Analytical Solution for Dynamic Fracture of Two Coplanar Limited-Permeable Cracks in Magneto-Electro-Elastic Material

Zhang¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Two coplanar limited-permeable rectangular cracks in magneto-electro-elastic material are modeled and solved using generalized Almansi's theorem. The mixed boundary value problem is formulated into three pairs of dual integral equations with the help of Fourier transform, in which the unknown functions are the jumps of displacements across the crack-surface. By directly expanding the unknown functions into infinite series form of Jacobi polynomials, the dual integral equations are solved, and the analytical expressions of generalized intensity factors are derived strictly. Based on the generalized intensity factors, the dynamic behaviors of two cracks are estimated under P-wave loads. To show the trends of effects of loading frequency and geometry of cracks on the generalized intensity factors, top finite terms of infinite series are numerically calculated based on the Schmidt method. Numerical results are then drawn graphically. It reveals that the trend of two cracks forming a larger crack by propagating depends strongly on crack geometry and load frequency. This work illuminate the condition inducing different crack propagation patterns, which will benifit the forecast of damage forms of transversely isotropic magneto-electro-elastic material.

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“…Moreover, although the problem of two collinear cracks in a magnetoelectroelastic solid has been investigated by Zhou et al [32], in the adopted limited-permeable boundary conditions, the negative signs are missing and the obtained results are some series solutions. The present paper is focused on the closed-form solutions for two collinear dielectric cracks in a magnetoelectroelastic material by using the semi-permeable magnetoelectric boundary conditions (1).…”

Section: Introductionmentioning

confidence: 96%

Closed-form solutions for two collinear dielectric cracks in a magnetoelectroelastic solid

Zhong

2011

Applied Mathematical Modelling

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a b s t r a c tThe problem of two collinear electromagnetically dielectric cracks in a magnetoelectroelastic material is investigated under in-plane electro-magneto-mechanical loadings. The semi-permeable crack-face boundary conditions are adopted to simulate the case of two collinear cracks full of a dielectric interior. Utilizing the Fourier transform technique, the boundary-value problem is reduced to solving singular integral equations with Cauchy kernel, which then are solved explicitly. The intensity factors of stress, electric displacement, magnetic induction, crack opening displacement (COD) and the energy release rates near the inner and outer crack tips are determined in closed forms for two cases of possible far-field electro-magneto-mechanical loadings respectively. Numerical results for a BaTiO 3 -CoFe 2 O 4 composite are carried out to show the effects of applied mechanical loadings on the crack-face electric displacement and magnetic induction, the stress intensity factor and the COD intensity factor, respectively. The obtained results reveal that when the applied mechanical loading is stress, applied electromagnetic loadings have no influences on the stress intensity factor. When the applied mechanical loadings is train, the applied positive electromagnetic loadings decrease the intensity factors of stress and COD, and the applied negative ones increase the intensity factors of stress and COD. The variations of energy release rates are also given to show the effects of the geometry of two collinear dielectric cracks.

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

Cited by 28 publications

References 40 publications

Transient response of a magnetoelectroelastic solid with two collinear dielectric cracks under impacts

Transient response of a magnetoelectroelastic solid with two collinear dielectric cracks under impacts

Analytical Solution for Dynamic Fracture of Two Coplanar Limited-Permeable Cracks in Magneto-Electro-Elastic Material

Closed-form solutions for two collinear dielectric cracks in a magnetoelectroelastic solid

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