Torsion of a flexoelectric semiconductor rod with a rectangular cross section

Qu, Yu; Jin, Feng; Yang, Jiashi

doi:10.1007/s00419-020-01867-0

Cited by 36 publications

(13 citation statements)

References 38 publications

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“…These have also become an active research topic in mechanics [10]. In contrast, the study on flexoelectric semiconductors is still at its beginning stage with limited results from semiconductor devices [11][12][13][14] and mechanics researchers [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Magnetically‐induced electromechanical fields in a flexoelectric semiconductor layer between two piezomagnetic dielectric layers

Jin

Yang

2022

Z Angew Math Mech

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We study magnetically-induced electromechanical fields in a sandwich plate of a flexoelectric semiconductor layer between two piezomagnetic dielectric layers under a transverse magnetic field. A set of two-dimensional equations for the bending of the plate is derived from the three-dimensional macroscopic theory of piezomagnetics and flexoelectric semiconductors. A few solutions from the plate equations are obtained for static and time-harmonic magnetic loadings. Resultsshow that various distributions of mobile charges and electric fields can be created by different magnetic fields, which is the foundation for flexotronics when magnetic fields are involved. In the case of pure bending under a uniform magnetic field, a combination of physical and geometric parameters is identified as a coefficient characterizing the strength of the interaction between the applied magnetic field and the mobile charges. The coefficient assumes a maximum for a particular thickness ratio between the two types of material layers. The frequency dependence of the coupling coefficient in time-harmonic motions is also obtained.

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Section: Introductionmentioning

confidence: 99%

Magnetically‐induced electromechanical fields in a flexoelectric semiconductor layer between two piezomagnetic dielectric layers

Jin

Yang

2022

Z Angew Math Mech

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“…Maranganti et al [5] proposed the general formulation based on the polarization gradient and strain gradient theories. Recently, this three-dimensional framework of strain gradient-based flexoelectricity theory was applied to analytically solve static bending and torsion problems of beams (rods) [30–33]. Li et al [34] proposed a general flexoelectricity theory within the framework of the couple stress and polarization gradient theories for isotropic dielectrics.…”

Section: Introductionmentioning

confidence: 99%

A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

Zhang

Fan

et al. 2021

Mathematics and Mechanics of Solids

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A new non-classical theory of elastic dielectrics is developed using the couple stress and electric field gradient theories that incorporates the couple stress, quadrupole and curvature-based flexoelectric effects. The couple stress theory and an extended Gauss’s law for elastic dielectrics with quadrupole polarization are applied to derive the constitutive relations of this new theory through energy conservation. The governing equations and the complete boundary conditions are simultaneously obtained through a variational formulation based on the Gibbs-type variational principle. The constitutive relations of general anisotropic and isotropic materials with the corresponding independent material constants are also provided, respectively. To illustrate the newly proposed theory and to show the flexoelectric effect in isotropic materials, one pure bending problem of a simply supported beam is analytically solved by directly applying the formulas derived. The analytical results reveal that the flexoelectric effect is present in isotropic materials. In addition, the incorporation of both the couple stress and flexoelectric effects always leads to increased values of the beam bending stiffness.

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“…Giannakopoulos et al [11] introduced an antiplane dynamic flexoelectric issue, which was defined as a dielectric solid with electric polarization and flexoelectricity gradients owing to strain gradients. Qu and colleagues [12] investigated the torsion of a rectangular cross-sectional flexoelectric semiconductor rod. It was based on the macroscopic theory of flexoelectric semiconductors.…”

Section: Introductionmentioning

confidence: 99%

“…Fig 12. The distribution of the electric field E z along the thickness direction with different values of f 14…”

mentioning

confidence: 99%

Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects

et al. 2021

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This paper uses the finite element method to simulate the mechanical, electric, and polarization behaviors of piezoelectric nanoplates resting on elastic foundations subjected to static loads, in which the flexoelectric effect is taken into consideration. The finite element formulations are established by employing a new type of shear deformation theory, which does not need any shear correction factors, but still accurately describes the stress field of the plate. The numerical results show clearly that the flexoelectric effect has a strong influence on the mechanical responses of the nanoplates. In particular, the normal stress distribution in the thickness direction is no longer linear when the flexoelectric coefficient is large enough, and this phenomenon differs completely from that of conventional plates. In addition, the distribution of the electric field and the polarization also depend on boundary conditions, which were not investigated in the published works.

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Torsion of a flexoelectric semiconductor rod with a rectangular cross section

Cited by 36 publications

References 38 publications

Magnetically‐induced electromechanical fields in a flexoelectric semiconductor layer between two piezomagnetic dielectric layers

Magnetically‐induced electromechanical fields in a flexoelectric semiconductor layer between two piezomagnetic dielectric layers

A non-classical theory of elastic dielectrics incorporating couple stress and quadrupole effects: part I – reconsideration of curvature-based flexoelectricity theory

Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects

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