Electric-Elastic Field Induced by a Straight Dislocation in One-Dimensional Quasicrystals

Yang, Lianzhi; Gao, Yang; Pan, Ernian; Waksmanski, Natalie

doi:10.12693/aphyspola.126.467

Cited by 20 publications

(14 citation statements)

References 15 publications

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“…The equilibrium equations, geometry equations, and constitutive equations for a 1D hexagonal piezoelectric quasicrystal, for which the periodic plane is the ( 1 , 3 )− plane, and the quasiperiodic and poling directions are along the 2 -axis, are given by: [5,19] , = 0, , = 0, 2 , = 0,…”

Section: Stroh Formalismmentioning

confidence: 99%

“…Based on extending the Stroh formalism to the deformation of 1D piezoelectric QCs, [19,29] when are functions of 1 and 2 only, the general solution is given by…”

Section: Appendix: Stroh Formalism Of 1d Piezoelectric Qcsmentioning

confidence: 99%

“…Using the Stroh formalism, Li and Liu [18] derived the elastic displacement and stress fields induced by a dislocation in an icosahedral quasicrystal. Yang et al [19] used the generalized Stroh formalism to study the electric-elastic fields around a straight dislocation in a 1D hexagonal quasicrystal. Li and Fan [20] investigated the dislocations and solutions for the second kind of 2D quasicrystals of soft matter.…”

Section: Introductionmentioning

confidence: 99%

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Fundamental solution for extended dislocation in one‐dimensional piezoelectric quasicrystal and application to fracture analysis

Fan

Chen

et al. 2019

Z Angew Math Mech

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In this paper, we derive a fundamental solution for extended dislocations of onedimensional (1D) hexagonal piezoelectric quasicrystals. Based on the Stroh formalism, the fundamental solutions for 1D hexagonal piezoelectric quasicrystals expressing by extended dislocations, including phonon, electric, and phason dislocations, are obtained. Then, by considering the continuously distributed dislocations to be a crack, the crack opening displacement, intensity factor, and energy release rate of the extended dislocation are expressed. Numerical calculations are used to confirm the validity of the theory and to investigate the effect of different parameters on the energy release rate. K E Y W O R D S crack, energy release rate, extended dislocation, fundamental solutions, one-dimensional piezoelectric quasicrystals Z Angew Math Mech. 2019;99:e201800232.

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Section: Stroh Formalismmentioning

confidence: 99%

“…Based on extending the Stroh formalism to the deformation of 1D piezoelectric QCs, [19,29] when are functions of 1 and 2 only, the general solution is given by…”

Section: Appendix: Stroh Formalism Of 1d Piezoelectric Qcsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fundamental solution for extended dislocation in one‐dimensional piezoelectric quasicrystal and application to fracture analysis

Fan

Chen

et al. 2019

Z Angew Math Mech

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“…Wang and Pan [12] employed the underlying investigation of the physical property tensors of Li and Liu [13] to determine elementary representations for the electroelastic field components of a screw dislocation moving uni-formly in one-dimensional hexagonal piezoelectric quasicrystals. Stroh's generalized formalism was applied by Yang et al [14] to obtain and numerically investigate the electric-elastic field of a stationary straight dislocation.…”

Section: Introductionmentioning

confidence: 99%

Non-Uniformly Loaded Row of Moving, Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

Tupholme

2018

Acta Phys. Pol. A

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An antiplane shear deformation in one-dimensional piezoelectric quasicrystals created by a row of collinear cracks subject to non-uniform phonon, phason and electric displacement loads is analyzed using a generalized technique of dislocation layers. Closed-form expressions are derived for the components of the phonon and phason stress and electric displacement fields. Their variations with angle near a crack tip are demonstrated and the corresponding phonon and phason stress and electric displacement intensity factors are deduced. Previously constantly loaded rows of cracks in various media have been studied. But no explicit expressions for the field components at a general point nor their angular variations were presented for them; even in classical isotropic elastic solids. The material considered here is the currently most general that is amenable to such an investigation and some of the analogous results for non-quasicrystals or non-piezoelectric or purely elastic solids or stationary cracks that can be deduced as particular cases are outlined. Some illustrative numerical results are graphically presented.

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“…e underpinning results of Li and Liu [14] on the physical property tensors enabled Wang and Pan [15] to give detailed closed-form representations of the field components of a screw dislocation moving uniformly in onedimensional hexagonal piezoelectric quasicrystals. Yang et al [16] obtained and investigated numerically the electric/elastic field of a straight stationary dislocation based upon the generalized Stroh formalism.…”

Section: Introductionmentioning

confidence: 99%

Nonuniformly Loaded Stack of Antiplane Shear Cracks in One‐Dimensional Piezoelectric Quasicrystals

Tupholme

2018

Advances in Materials Science and Engineering

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Representations in a closed form are derived, using an extension to the method of dislocation layers, for the phonon and phason stress and electric displacement components in the deformation of one-dimensional piezoelectric quasicrystals by a nonuniformly loaded stack of parallel antiplane shear cracks. Their dependence upon the polar angle in the region close to the tip of a crack is deduced, and the field intensity factors then follow. These exhibit that the phenomenon of crack shielding is dependent upon the relative spacing of the cracks. The analogous analyses, that have not been given previously, involving non-piezoelectric or non-quasicrystalline or simply elastic materials can be straightforwardly considered as special cases. Even when the loading is uniform and the crack is embedded in a purely elastic isotropic solid, no explicit representations have been available before for the components of the field at points other than directly ahead of a crack. Typical numerical results are graphically displayed.

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Electric-Elastic Field Induced by a Straight Dislocation in One-Dimensional Quasicrystals

Cited by 20 publications

References 15 publications

Fundamental solution for extended dislocation in one‐dimensional piezoelectric quasicrystal and application to fracture analysis

Fundamental solution for extended dislocation in one‐dimensional piezoelectric quasicrystal and application to fracture analysis

Non-Uniformly Loaded Row of Moving, Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

Nonuniformly Loaded Stack of Antiplane Shear Cracks in One‐Dimensional Piezoelectric Quasicrystals

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