Symmetry of flexoelectric coefficients in crystalline medium

Shu, Longlong; Wei, Xiaoyong; Ting, Pang; Yao, Xi; Wang, Chunlei

doi:10.1063/1.3662196

Cited by 182 publications

(78 citation statements)

References 9 publications

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“…By substituting Eqs. (30)(31)(32)(33) into Eq. (21), we can rewrite the governing equation in terms of the transverse displacement w as …”

Section: Governing Equationsmentioning

confidence: 98%

“…where f 14 = f 3113 and f 14 = f 3223 are introduced for convenience [30]. Only the strain gradients along the thickness direction, η x xz = − ∂ 2 w ∂ x 2 and η yyz = − ∂ 2 w ∂ y 2 , are taken into account, while all the other strain gradients are ignored since the associated flexoelectric coefficients are equal to zero or strain gradients are much smaller than those along the thickness direction.…”

Section: Governing Equationsmentioning

confidence: 99%

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Electromechanical responses of piezoelectric nanoplates with flexoelectricity

Yang

Shen

2015

Acta Mech

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Flexoelectricity, representing the coupling between electrical polarizations and strain gradients, should be taken into account in the analysis of electromechanical responses of nanostructures where large strain gradients are expected. In this paper, we will explore the influence of flexoelectricity on the electromechanical coupling behavior of a simply supported piezoelectric nanoplate by using the Kirchhoff plate theory. The governing equations and corresponding boundary conditions are deduced from Hamilton's principle, and the analytical solutions are obtained for the deflection and natural frequency. The results indicate that the deflections predicted by the present model are smaller than those calculated by the classical one which only considers piezoelectricity, while the frequencies exhibit the opposite trend. In addition, the flexoelectric effect is more prominent for thinner plates; the differences of the deflections or frequencies between the two models are gradually diminishing with an increase in the plate thickness. The current work may contribute to the understanding of the higher-order electromechanical coupling mechanism. Moreover, the modified plate model can be utilized to accurately design novel piezoelectric nanoplate-based sensors in nanoelectromechanical systems.

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“…By substituting Eqs. (30)(31)(32)(33) into Eq. (21), we can rewrite the governing equation in terms of the transverse displacement w as …”

Section: Governing Equationsmentioning

confidence: 98%

Section: Governing Equationsmentioning

confidence: 99%

Electromechanical responses of piezoelectric nanoplates with flexoelectricity

Yang

Shen

2015

Acta Mech

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“…The number of their independent components is controlled by the symmetry of the material (see, e.g., Refs. [27][28][29]. For example, this number is 2 for isotropic materials and 3 for non-piezoelectric cubic materials.…”

Section: Dynamic Responsementioning

confidence: 99%

Flexoelectric Effect in Solids

Zubko

Catalán

Tagantsev

2013

Annu. Rev. Mater. Res.

851

663

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Piezoelectricity-the coupling between strain and electrical polarization, allowed 2 Zubko, Catalan, Tagantsev by symmetry in a restricted class of materials-is at the heart of many devices that permeate our daily life. Since its discovery in the 1880's by Pierre and Jacques Curie, the piezoelectric effect has found use in everything from submarine sonars to cigarette lighters. By contrast, flexoelectricity-the coupling between polarization and strain gradients, allowed by symmetry in all materials-was largely overlooked for decades since its first proposal in the late 1950's, due to the seemingly small magnitude of the effect in bulk. The development of nanoscale technologies, however, has renewed the interest in flexoelectricity, as the large strain gradients often present at the nanoscale can lead to dramatic flexoelectric phenomena. Here we review the fundamentals of the flexoelectric effect, discuss its presence in many nanoscale systems, and look at potential applications of this fascinating phenomenon. The review will also emphasize the many open questions and unresolved issues in this developing field.

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“…6 are employed. For flexoelectric coefficients, Le Quang and He [24] represented all the possible rotational symmetries for flexoelectric tensors, Shu et al [25] discussed the symmetry of flexoelectric coefficient in crystalline medium. We assume the flexoelectric coefficient as follows for sake of simplicity [25,26] …”

Section: Timoshenko Beam Model With Flexoelectricitymentioning

confidence: 99%

A Timoshenko dielectric beam model with flexoelectric effect

Zhang

Shen

2015

Meccanica

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In this paper, a Timoshenko dielectric beam model with the consideration of the direct flexoelectric effect is developed by using the variational principle. The governing equations and the corresponding boundary conditions are naturally derived from the variational principle. The effect of flexoelectricity on the Timoshenko dielectric beams is analytically investigated. The developed beam model recovers to the classical Timoshenko beam model when the flexoelectricity is not taken into account. To illustrate this model, the deflection and rotation of Timoshenko dielectric nanobeam under two different boundary conditions are calculated. The numerical results reveal that both the deflection and rotation predicted by the current model are smaller than those predicted by the classical Timoshenko beam model. Moreover, the discrepancies of the deflection and rotation between the values predicted by the two models are very large when the beam thickness is small. The current model can also reduce to the Bernoulli-Euler dielectric beam model wherein the shear deflection is not considered. This work may be helpful in understanding the electromechanical response at nanoscale and designing dielectric devices.

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Symmetry of flexoelectric coefficients in crystalline medium

Cited by 182 publications

References 9 publications

Electromechanical responses of piezoelectric nanoplates with flexoelectricity

Electromechanical responses of piezoelectric nanoplates with flexoelectricity

Flexoelectric Effect in Solids

A Timoshenko dielectric beam model with flexoelectric effect

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