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

Qu, Yu; Zhang, Gongye; Fan, YM; Jin, Feng

doi:10.1177/10812865211001533

Cited by 40 publications

(35 citation statements)

References 41 publications

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“…where p i , τ 1 ijk and m s ij are the work conjugate of γ i , η 1 ijk and χ s ij , respectively. We note that there are several possible formulations available in literature [22,27,[46][47][48][49][50].…”

Section: Representation Of Gradient Effects In Terms Of Length Scale ...mentioning

confidence: 99%

A gradient electromechanical theory for thin dielectric curved beams considering direct and converse flexoelectric effects

Joshan

Santapuri

2022

Z. Angew. Math. Phys.

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This work presents the development of a unified gradient electromechanical theory for thin flexoelectric beams considering both direct and converse flexoelectric effects. The two-way coupled electromechanical theory is developed starting from 3D variational formulation by considering an electric field-strain based free energy function. The formulation incorporates mechanical as well as electrical size effects. The coupled 3D theory is specialized to isotropic materials and a 1D beam theory for composite flexoelectric curved beams is derived using the classical Kirchhoff assumptions. The beam theory is solved using a novel C 2 continuous finite element framework for different loading and boundary conditions. Our finite element results are verified with analytical solutions for a simply-supported flexoelectric beam operating in both actuator and sensor modes. The results are also compared with existing literature for the special case of a passive micro-beam. Our computational framework is subsequently used to perform various parametric studies to analyze the effect of electrical and mechanical length scale parameters, geometric parameters like the radius of curvature, flexoelectric layer thickness etc., on the response of the beam. Also, contribution of converse flexoelectricity in the overall response of the flexoelectric beam is compared with that of the direct effect. Our simulation results predict that the converse effect is significant (≈ 10-25% of the direct effect) for a wide range of thickness and length scale parameter values. It is also observed that the effective electromechanical coupling coefficient, calculated in terms of the voltage developed across the flexoelectric layer thickness, is higher in flexoelectric materials compared to piezoelectric materials at smaller length scales (thickness of the order of a few microns). Our simulation results also agree well with the trends observed in recent experimental work [1].

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Section: Representation Of Gradient Effects In Terms Of Length Scale ...mentioning

confidence: 99%

A gradient electromechanical theory for thin dielectric curved beams considering direct and converse flexoelectric effects

Joshan

Santapuri

2022

Z. Angew. Math. Phys.

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“…The first variation of the Gibbs-type energy for the deformed MEE Kirchhoff plate is given by [31]  …”

Section: Formulationmentioning

confidence: 99%

“…Applying the Gibbs-type variational principle and the fundamental lemma of the calculus of variations [31], the governing equations result in…”

Section: Formulationmentioning

confidence: 99%

A Transversely Isotropic Magneto-Electro-Elastic Circular Kirchhoff Plate Model Incorporating Microstructure Effect

Shen

Zhang

et al. 2021

Acta Mech. Solida Sin.

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A non-classical model for transversely isotropic magneto-electro-elastic circular Kirchhoff plates is established based on the extended modified couple stress theory. The Gibbs-type variational principle is used to obtain the governing equations and boundary conditions. To illustrate the newly derived model, the static bending problem of a clamped circular plate subjected to a uniformly distributed constant load is solved numerically by Fourier-Bessel series. The numerical results show that the values of transverse displacement, electric and magnetic potentials predicted by the current model are always smaller than those of the classical model, and the differences are diminishing as the plate thickness increases. In addition, it is shown that the magneto-electro-elastic coupling effect plays an important role in the transverse displacement, electric potential and magnetic potential of the magneto-electro-elastic circular Kirchhoff plates. Furthermore, several reduced specific models are provided for simpler cases.

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“…Thus, it is important to investigate the MEEFGP microstructure based on nonclassical theories. During the past few decades, many theories have been developed to deal with the size effect by introducing additional material parameters, such as nonlocal theory [21], couple stress theory [22][23][24], strain gradient theory [25][26][27], and a series of simpler versions [28][29][30][31][32][33]. Based on the nonlocal theory, numerous MEE/MEEFGM/MEEFGP structures have been developed, taking the nonlocal size effect into account [34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Bending and Wave Propagation Analysis of Magneto-Electro-Elastic Functionally Graded Porous Microbeams

et al. 2022

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In this paper, a microstructure-dependent magneto-electro-elastic functionally graded porous (MEEFGP) beam model is proposed using a variational approach. To account for the microstructure effect, the extended modified couple stress theory is incorporated in the new model. In addition, the porosity variation of the two-phase beam model through the thickness direction is also considered. The new developed model is verified in terms of its correctness with a FEM model. Based on the equations of motion and boundary conditions derived by Hamilton’s principle, the static bending and wave propagation behaviors of the new model are analytically determined. The results prove the existence of the microstructure effect and the magneto-electro-elastic multi-field coupling effect. There are significant differences between the new model and the classical model at the microscale. Moreover, the porosity also has an important influence on the mechanical properties of the new model. The results predicted by the new model can provide the theoretical basis for the design of microscale acoustic wave devices and micro-electro-mechanical systems.

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

Cited by 40 publications

References 41 publications

A gradient electromechanical theory for thin dielectric curved beams considering direct and converse flexoelectric effects

A gradient electromechanical theory for thin dielectric curved beams considering direct and converse flexoelectric effects

A Transversely Isotropic Magneto-Electro-Elastic Circular Kirchhoff Plate Model Incorporating Microstructure Effect

Bending and Wave Propagation Analysis of Magneto-Electro-Elastic Functionally Graded Porous Microbeams

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