General solutions of mechanical‐electric‐magnetic fields in magneto‐electro‐elastic solid containing a moving anti‐plane crack and a screw dislocation

Wang, Y.-Z.; Kuna, Meinhard

doi:10.1002/zamm.201300279

Cited by 8 publications

(4 citation statements)

References 35 publications

(54 reference statements)

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“…We focus on the calculation of the stress intensity factor, electric displacement intensity factor, and magnetic induction intensity factor at the crack tip. By using the definition of Wang and Kuna [31], the generalized mode III stress intensity factor at the crack tip is defined as…”

Section: Generalized Intensity Factormentioning

confidence: 99%

“…Jiang et al [28,29] studied the magneto-electro-elastic interference between a screw dislocation and an elliptic inclusion with a confocal rigid line in piezoelectromagnetic composites. Wang and Kuna [30,31] considered the screw dislocation in functionally graded magnetoelectro-elastic solids and researched the mechanical electromagnetic interaction of a screw dislocation and a moving anti-plane crack. Shen and Hung [32] studied a screw dislocation interacting with a wedge crack penetrating a fibrous three-phase magneto-electro-elastic composite.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Interaction between a generalized screw dislocation in the matrix and an inhomogeneity containing an elliptic hole in piezoelectric–piezomagnetic composite materials

Peng

Yang

2019

Mathematics and Mechanics of Solids

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The paper deals with the interaction of a generalized screw dislocation and an elliptic inhomogeneity containing a confocal elliptic hole in a magneto-electro-elastic composite material. Exact solutions are derived for the case where the generalized screw dislocation is located in the matrix under a remote anti-plane shear stress field, an in-plane electric field, and a magnetic field. Based on the complex variable method, the complex potentials of both the matrix and the inhomogeneity are obtained in series, and analytic expressions for the generalized stress and strain field, the image force, the generalized stress intensity factor of the blunt crack tip, and the energy release rate are derived explicitly. The presented solutions include some previous solutions, such as pure elastic, piezoelectric, piezomagnetic, and circular inclusions. Typical numerical examples are presented and the influences of the dislocation position, the volume of inhomogeneity, and the elliptic hole on these physical quantities are discussed. The results show that the magneto-electro-elastic coupling effect has a great influence on the image force and the equilibrium position of dislocation, especially when the dislocation approaches the interface; the coupling effect makes the image force on the screw dislocation follow different variation laws in piezoelectric–piezomagnetic composite materials compared with elastic materials.

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Section: Generalized Intensity Factormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interaction between a generalized screw dislocation in the matrix and an inhomogeneity containing an elliptic hole in piezoelectric–piezomagnetic composite materials

Peng

Yang

2019

Mathematics and Mechanics of Solids

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“…At present, considerable progress has been made in researches of magnetoelectric materials, especially for their Green's functions and fundamental solutions. The method of Green's functions can be used to study the mechanical behaviors or defects of magnetoelectric materials [12][13][14][15][16][17][18][19][20][21]. Wang and Shen [22] and Hou et al [23] derive the three-dimensional Green's functions of the semi-infinite magnetoelectroelastic body.…”

Section: Introductionmentioning

confidence: 99%

Green’s functions of steady-state transversely isotropic hygro-thermo-magneto-piezoelectric cones

Zhang

Fan

Han³

et al. 2022

Mathematics and Mechanics of Solids

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Green’s functions of transversely isotropic hygro-thermo-magneto-piezoelectric (HTMP) cones are established. The governing equations of transversely isotropic HTMP media are first simplified by introducing two displacement functions. Steady-state general solutions of transversely isotropic HTMP media expressed by seven quasi-harmonic functions are obtained by the operator theory, superposition principle, and generalized Almansi’s theorem. Furthermore, the three-dimensional problems of a semi-infinite HTMP cone subjected to a point moisture source and a point heat source are analyzed by introducing the potential functions which are determined by moisture, thermal, electric, magnetic equilibrium relationships and boundary conditions. Furthermore, the fundamental solutions of the HTMP cones under the action of the point sources are obtained. The numerical examples and the contours of the coupled fields of HTMP cones are presented, and the variation regularity of stress, electric displacement, and magnetic induction are discussed. The effects of different apex angles of cones on the coupled fields are also analyzed.

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“…Viun studied the problem for a periodic set of the limited electrically and magnetically permeable cracks in magneto‐electro‐elastic media. Wang and Kuna derived the exact solution of interaction between a screw dislocation and a moving anti‐plane crack in magneto‐electro‐elastic solids. Shen and Hung investigated the magneto‐electro‐mechanical interaction problem between a generalized screw dislocation and a fibrous three‐phase composite penetrated by a semi‐infinite wedge crack.…”

Section: Introductionmentioning

confidence: 99%

Generalized screw dislocations interacting with interfacial secondary crack in magneto‐electro‐elastic solid

Zeng

Liu

et al. 2019

Z Angew Math Mech

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The interaction between generalized screw dislocation and two asymmetrical interfacial secondary cracks emanating from an elliptic blunt crack tip in magneto‐electro‐elastic solid is investigated. Utilizing the complex potential method, the closed‐form solutions for complex potentials and generalized stress fields are derived. In some limiting cases, the present solutions can reduce to the well‐known results. Moreover, many new solutions for special cases are discussed. The energy release rate at the right interfacial secondary crack tip and the image force acting on dislocation are also calculated. Numerical calculations are given for analyzing the effects of variable parameters, such as location of the dislocation, materials constants and geometrical parameters of interfacial secondary crack. The results show that the long left interfacial secondary crack or the blunt crack with the high passivation rate enhances the influence of the dislocation on the energy release rate at the right interfacial secondary crack tip. In addition, the energy release rate increases with the increment of elastic coefficient of the other half‐plane, but decreases with the increment of dielectric coefficient or magnetic permeability coefficient.

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General solutions of mechanical‐electric‐magnetic fields in magneto‐electro‐elastic solid containing a moving anti‐plane crack and a screw dislocation

Cited by 8 publications

References 35 publications

Interaction between a generalized screw dislocation in the matrix and an inhomogeneity containing an elliptic hole in piezoelectric–piezomagnetic composite materials

Interaction between a generalized screw dislocation in the matrix and an inhomogeneity containing an elliptic hole in piezoelectric–piezomagnetic composite materials

Green’s functions of steady-state transversely isotropic hygro-thermo-magneto-piezoelectric cones

Generalized screw dislocations interacting with interfacial secondary crack in magneto‐electro‐elastic solid

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