A Closed Form Solution of a Crack in Magneto-Electro-Elastic Composites under Anti-Plane Shear Stress Loading

Zhou, Zhen-Gong; Wu, Linzhi; Wang, Biao

doi:10.1299/jsmea.48.151

Cited by 9 publications

(8 citation statements)

References 10 publications

(6 reference statements)

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“…It is observed that for the permeable condition, the stress, electric and magnetic intensity factors of a cluster of multiple cracks are independent from the electric and magnetic loadings. This characteristic of the generalized intensity factors for permeable crack in magnetoelectroelastic materials has been reported in the literature for single crack and also for the case of three parallel non‐symmetric cracks . It should be noted that for a mathematical permeable crack with zero width, Gao et al showed that the energy release rate is independent of the applied electric/magnetic loading.…”

Section: Dislocation‐based Analysis Of Planes With Electromagneticallsupporting

confidence: 64%

“…with kernels described after Eq. (28). It is noticed that for permeable condition, the stress field is identical to the stress field in an elastic solid.…”

Section: Field Components For System Of Permeable Cracksmentioning

confidence: 93%

“…Static fracture analysis of magnetoelectroelastic materials has been discussed in some recent papers. Zhou et al provided a closed form solutions of a crack in magnetoelectroelastic composites under anti‐plane shear stress loading. They assumed that the crack surfaces are in perfect contact which leads to continuous normal electric displacement, electric potential, the magnetic flux and the magnetic potentials across the crack surfaces.…”

Section: Introductionmentioning

confidence: 99%

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Dislocation‐based fracture analysis of functionally graded magnetoelectroelastic solids

Mousavi

2015

Z Angew Math Mech

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Dislocation‐based analysis of cracked magnetoelectroelastic solid under remotely uniform anti‐plane mechanical with in‐plane electromagnetic loading is presented. The solution to the generalized dislocation including screw dislocation and electric and magnetic jumps within an incompatible framework are reviewed from the literature. In order to model the system of multiple cracks in the solid, the dislocations are distributed along the crack faces. Then the densities of the dislocations are evaluated by applying the crack‐face boundary conditions. Both permeable and impermeable conditions are discussed. The entire field components including shear stress, electric displacements and magnetic inductions are determined for the cracked material, which is an advantage comparing to the methods which only provide crack tip field components. The field intensity factors are also formulated for both permeable and impermeable conditions. Finally examples including horizontal crack, inclined crack and multiple cracks are studied.

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Section: Dislocation‐based Analysis Of Planes With Electromagneticallsupporting

confidence: 64%

“…with kernels described after Eq. (28). It is noticed that for permeable condition, the stress field is identical to the stress field in an elastic solid.…”

Section: Field Components For System Of Permeable Cracksmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Dislocation‐based fracture analysis of functionally graded magnetoelectroelastic solids

Mousavi

2015

Z Angew Math Mech

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“…The crack problems of multi-ferroic materials have gained significant interest from many researchers in the past two decades. Considerable academic efforts have been made on the analytical works for two-and three-dimensional crack problems, i.e., planar or anti-plane cracks [7,8,10,[12][13][14][15][16][17][18][19], penny-shaped cracks [20][21][22][23][24], elliptical cracks [25,26], and so forth.…”

Section: Introductionmentioning

confidence: 99%

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

Zheng¹,

Wu²,

Li³

et al. 2018

Smart Mater. Struct.

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The problem of a penny-shaped crack embedded in an infinite space of transversely isotropic multi-ferroic composite medium is investigated. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. The semi-permeable (limited-permeable) electro-magnetic boundary condition is adopted. By virtue of the generalized method of potential theory and the general solutions, the boundary integro-differential equations governing the mode I crack problem, which are of nonlinear nature, are established and solved analytically. Exact and complete coupling magneto-electro-elastic field is obtained in terms of elementary functions. Important parameters in fracture mechanics on the crack plane, e.g., the generalized crack surface displacements, the distributions of generalized stresses at the crack tip, the generalized stress intensity factors and the energy release rate, are explicitly presented. To validate the present solutions, a numerical code by virtue of finite element method is established for 3D crack problems in the framework of magneto-electro-elasticity. To evaluate conveniently the effect of the medium inside the crack, several empirical formulae are developed, based on the numerical results.

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“…Based on the Stroh formalism method, the 2D Green's functions in EMTE media were given by Qin (2005). Zhou and Wang (2004) and Zhou et al (2005) studied a permeable crack subjected to an anti-plane shear loading by the Fourier transform method, and then found that the stress field was independent of the electric field and the magnetic flux.…”

Section: Introductionmentioning

confidence: 99%

Application of hypersingular integral equation method to three-dimensional crack in electromagnetothermoelastic multiphase composites

Zhu

Tong

2007

International Journal of Solids and Structures

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A three-dimensional crack problem in electromagnetothermoelastic multiphase composites (EMTE-MCs) under extended loads is investigated in this paper. Using Green's functions, the extended general displacement solutions are obtained by the boundary element method. This crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations, in which the unknown functions are the extended displacement discontinuities. Then, the behavior of the extended displacement discontinuities around the crack front terminating at the interface is analyzed by the main-part analysis method of hypersingular integral equations. Analytical solutions for the extended singular stresses, the extended stress intensity factors (SIFs) and the extended energy release rate near the crack front in EMTE-MCs are provided. Also, a numerical method of the hypersingular integral equations for a rectangular crack subjected to extended loads is put forward with the extended displacement discontinuities approximated by the product of basic density functions and polynomials. In addition, distributions of extended SIFs varying with the shape of the crack are presented. The results show that the present method accurately yields smooth variations of extended SIFs along the crack front.

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A Closed Form Solution of a Crack in Magneto-Electro-Elastic Composites under Anti-Plane Shear Stress Loading

Cited by 9 publications

References 10 publications

Dislocation‐based fracture analysis of functionally graded magnetoelectroelastic solids

Dislocation‐based fracture analysis of functionally graded magnetoelectroelastic solids

Analytical and numerical analyses for a penny-shaped crack embedded in an infinite transversely isotropic multi-ferroic composite medium: semi-permeable electro-magnetic boundary condition

Application of hypersingular integral equation method to three-dimensional crack in electromagnetothermoelastic multiphase composites

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