Green's functions of one-dimensional quasicrystal bi-material with piezoelectric effect

Zhang, Liangliang; Wu, Di; Xu, Wenshuai; Yang, Lianzhi; Ricoeur, Andreas; Wang, Zhibin; Gao, Yang

doi:10.1016/j.physleta.2016.07.043

Cited by 43 publications

(13 citation statements)

References 33 publications

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“…The coupling constant has great influence on the mechanical behaviors of QCs, and it has not been measured yet. In the computation, the coupling constant of material 2 is assumed as (2) 3 = 0.8846 [21]. Other parameters are selected as follows:…”

Section: Numerical Resultsmentioning

confidence: 99%

Interaction of a Screw Dislocation with Interface and Wedge‐Shaped Cracks in One‐Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

Zhao

2019

Mathematical Problems in Engineering

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Interaction of a screw dislocation with wedge-shaped cracks in one-dimensional hexagonal piezoelectric quasicrystals bimaterial is considered. The general solutions of the elastic and electric fields are derived by complex variable method. Then the analytical expressions for the phonon stresses, phason stresses, and electric displacements are given. The stresses and electric displacement intensity factors of the cracks are also calculated, as well as the force on dislocation. The effects of the coupling constants, the geometrical parameters of cracks, and the dislocation location on stresses intensity factors and image force are shown graphically. The distribution characteristics with regard to the phonon stresses, phason stresses, and electric displacements are discussed in detail. The solutions of several special cases are obtained as the results of the present conclusion.

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Section: Numerical Resultsmentioning

confidence: 99%

Interaction of a Screw Dislocation with Interface and Wedge‐Shaped Cracks in One‐Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

Zhao

2019

Mathematical Problems in Engineering

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“…And , 2 and are called extended stresses, , and 2 are called extended displacements. Based on the extended Stroh formalism, [11,13,17,30] the extended displacements = ( 1 2 3 2 ) T and extended stress function vector can be expressed as…”

Section: Stroh Formalismmentioning

confidence: 99%

“…T A B L E 1 Material constants for the 1D hexagonal piezoelectric quasicrystal [9,31] Property 1D hexagonal piezoelectric QC Phonon elastic ( ) 11 = 150, 12 = 55, 13 The energy release rate can be expressed [8,31] = ∫ Γ (…”

Section: Crack Opening Displacement Intensit Y Factor and Energy Rementioning

confidence: 99%

“…Guo and Pan [10] derived the exact closed-form solutions of the stresses of the phonon and phason fields as well as the electric field for a three-phase cylinder model (inclusion/matrix/composite) of a 1D hexagonal piezoelectric quasicrystal composite. Zhang et al [11] obtained solutions of the internal and interfacial Green's functions of a quasicrystal bi-material based on the Stroh formalism of a 1D piezoelectric quasicrystal. Guo et al [12] analyzed an elliptical inclusion embedded in an infinite 1D hexagonal piezoelectric quasicrystal matrix in the framework of linear piezoelectricity of quasicrystals by using the technique of conformal mapping.…”

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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“…During 2016-18, the flourishing interest in piezoelectric effects of one-dimensional quasicrystals is demonstrated by ongoing publications. Zhang et al [18] presented Green's functions for bi-materials of piezoelectric quasicrystals. A three-phase cylinder model was proposed by Guo and Pan [19] for quasicrystal composites of onedimensional hexagonal piezoelectric quasicrystals.…”

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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Green's functions of one-dimensional quasicrystal bi-material with piezoelectric effect

Cited by 43 publications

References 33 publications

Interaction of a Screw Dislocation with Interface and Wedge‐Shaped Cracks in One‐Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

Interaction of a Screw Dislocation with Interface and Wedge‐Shaped Cracks in One‐Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

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

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