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

Zhong, Xian-Ci

doi:10.1016/j.apm.2010.12.010

Cited by 25 publications

(5 citation statements)

References 42 publications

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“…Mathematical Problems in Engineering Equation ( 31) is a singular integral equation including the Cauchy kernel [24], and the solution can be depicted as…”

Section: Solution Proceduresmentioning

confidence: 99%

The Analysis of a Cracked Material under Combined Unsymmetric Thermal Flux and Symmetric Linear Mechanical Loading

Huang

Peng

et al. 2021

Mathematical Problems in Engineering

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An improved partially permeable crack model is put forward to deal with the problem of a single crack embedded in an orthotropic or isotropic material under combined unsymmetric thermal flux and symmetric linear mechanical loading. With the application of the Fourier transform technique (FTT), the thermoelastic field is given in a closed form. Numerical results show combined unsymmetric linear thermal flux, symmetric linear mechanical loading, and dimensionless thermal conductivity, and the coefficient has influences on fracture parameters. For the improved partially permeable crack, the mode II stress intensity factor and the energy release rate might be zero or positive under combined unsymmetric thermal flux and symmetric linear mechanical loading. Therefore, closure of the crack tip region need not be considered under combined unsymmetric thermal flux and symmetric linear mechanical loading when making use of fracture parameters as a criterion.

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“…Mathematical Problems in Engineering Equation ( 31) is a singular integral equation including the Cauchy kernel [24], and the solution can be depicted as…”

Section: Solution Proceduresmentioning

confidence: 99%

The Analysis of a Cracked Material under Combined Unsymmetric Thermal Flux and Symmetric Linear Mechanical Loading

Huang

Peng

et al. 2021

Mathematical Problems in Engineering

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Section: Introductionmentioning

confidence: 99%

“…In addition to the above studies, multiple cracks problems [5–9, 22, 33–40] in any material are always important for study and designing any structure as crack‐interaction is one of the key parameters to enhance the crack‐growth in a solid. In MEE materials, various researchers have contributed in this direction including multiple collinear cracks problems [22, 33–37, 39–41]. Jangid [28] applied a particular case of EMPS model that is, considering magnetic saturation zone only for studying the two semipermeable cracks in MEE medium using Riemann–Hilbert approach.…”

Section: Introductionmentioning

confidence: 99%

Singular integral method based closed form solution for moving EMPS model in semipermeable two‐equal‐collinear cracked MEE material

Kumar,

Sharma,

Bui

2024

Z Angew Math Mech

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This paper presents the analytical closed‐form solutions of moving two equal collinear semipermeable cracks in magneto‐electro‐elastic material considering the strip electric‐magnetic polarization saturation (EMPS) model. To simulate the dynamic/moving cracks problem, two equal collinear Yoffe type cracks moving with a constant subsonic velocity along the plane of the cracks is considered. The problem is solved by considering semipermeable crack face conditions and under the in‐plane electro‐magnetic‐mechanical loading. Applying distributed dislocation technique and symmetry of the collinear cracks, the problem is reduced into simultaneous singular integral equations which have been solved in closed form expressions using finite Hilbert approach. The explicit expressions for dynamic distributed dislocation densities, crack opening displacement (COD), crack opening potential (COP), crack opening induction (COI), and local stress intensity factors (LSIFs) are evaluated for both the cases of the EMPS model (magnetic zone is smaller or greater than electric zone). For evaluation of inner and outer electric and magnetic zone lengths (MZLs), an iterative approach is applied to solve the developed two non‐linear equations. Also, to implement the semipermeable crack‐face conditions, a bisection iterative method has been applied. Based on the developed closed form solutions, numerical studies are presented for standard fracture parameters with respect to crack propagation velocity, electrical loading and inter‐crack space distance. This study shows that electric displacement and magnetic induction defined over the crack‐surface for semipermeable conditions decrease whereas the numerical values of saturated zone lengths, COD, COP, COI, and LSIFs increase with increasing crack propagation velocity. Moreover, for both static and dynamic cracks problems, the significant crack‐interaction effects have been observed on all the studied fracture parameters except the crack‐face conditions.

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“…studied the problem of two symmetric interface cracks between two dissimilar magneto‐electro‐elastic composite. Zhong obtained the closed‐form solution for the problem of two collinear electromagnetically dielectric cracks in a magneto‐electro‐elastic material. Tian and Gabbert investigated the macrocrack–microcrack interaction in magneto‐electro‐elastic solid.…”

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

Cited by 25 publications

References 42 publications

The Analysis of a Cracked Material under Combined Unsymmetric Thermal Flux and Symmetric Linear Mechanical Loading

The Analysis of a Cracked Material under Combined Unsymmetric Thermal Flux and Symmetric Linear Mechanical Loading

Singular integral method based closed form solution for moving EMPS model in semipermeable two‐equal‐collinear cracked MEE material

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

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