Static and dynamic analytical coupled field analysis of piezoelectric flexoelectric nanobeams: A strain gradient theory approach

Baroudi, Sourour; Najar, Fehmi; Jemai, Ahmed

doi:10.1016/j.ijsolstr.2017.11.014

Cited by 48 publications

(11 citation statements)

References 43 publications

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“…Such simplifications are convenient (and hence popular) in order to facilitate the derivations of closed-form analytical solutions for simple flexoelectric devices, e.g. Euler-Bernoulli beams [50][51][52][53][54] and Timoshenko beams 55 , and also to ease the implementation of numerical solution methods, e.g. the finite element (or related) methods.…”

Section: A Direct and Converse Flexoelectricitymentioning

confidence: 99%

Mathematical and computational modeling of flexoelectricity

Codony

Mocci

Barceló-Mercader

et al. 2021

Journal of Applied Physics

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We first revisit the mathematical modeling of the flexoelectric effect in the context of continuum mechanics at infinitesimal deformations. We establish and clarify the relation between the different formulations, point out theoretical and numerical issues related to the resulting boundary value problems, and present the natural extension to finite deformations. We then present a simple B-spline based computational technique to numerically solve the associated boundary value problems, which can be extended to handle unfitted meshes, hence allowing for arbitrarily-shaped geometries. Several numerical examples illustrate the flexoelectric effect in simple benchmark setups, as well as in new flexoelectric devices and metamaterials engineered for sensing or actuation.

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Section: A Direct and Converse Flexoelectricitymentioning

confidence: 99%

Mathematical and computational modeling of flexoelectricity

Codony

Mocci

Barceló-Mercader

et al. 2021

Journal of Applied Physics

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“…The main deal of such investigations relies on free vibration, buckling, instability and wave dispersion analysis of the Nano-structures in the geometry of beam, plate and tube. 47–53 Among these works, Chen and Yan 54 performed preliminary research as a first attempt to make a bridge between the flexoelectricity phenomenon and pull-in instability behavior in smart Nano-switches. Their system was an electrostatically-actuated cantilever nanobeam sandwiched with a piezoelectric layer.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear static pull-in instability analysis of smart nano-switch considering flexoelectric and surface effects via DQM

Masoumi

Amiri

Vesal

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper deals with the investigation of nonlinear static pull-in instability of smart Nano-switches regarding the new size-dependent phenomenon, known as flexoelectricity, together with the surface effects. It is noteworthy that the coupling effect of the flexoelectricity and surface elasticity on nonlinear static pull-in instability of electrostatically-actuated Nano-switches has not been studied before. Euler-Bernoulli beam assumptions in conjunction with the von-Karman nonlinearity are considered to formulate the problem. The Nano-switch is subjected to electrostatic actuation force with fringing field effect as well as Casimir force. Refined constitutive relations for piezoelectric materials capturing the flexoelectric effects are taken into consideration for mathematical modeling. Additionally, a surface elasticity approach is employed to reach an accurate model for the system. Considering the imposed electric boundary conditions, Gauss’s equation is solved to acquire the electric potential distribution along with the thickness of the Nano-switch. Thereafter, Hamilton’s principle is hired to derive the coupled nonlinear governing equations of the system. Utilizing the differential quadrature method (DQM), the nonlinear ordinary differential equations are transformed into a system of nonlinear algebraic equations. Consequently, Newton-Raphson method is exploited as a numerical method to solve the obtained algebraic equations which leads to the pull-in voltage. Investigating the maximum displacement of the Nano-switch in response to the applied electrostatic force, the effects of various involved parameters such as flexoelectricity and surface elasticity on pull-in instability are explored in detail. Furthermore, the size-dependent behavior of the pull-in instability against the flexoelectric, surface effects and applied piezoelectric voltage is analyzed. Totally, it is revealed that the flexoelectricity may exhibit a substantial influence on the pull-in behavior of smart Nano-switches, especially for some cases with small thicknesses. Therefore, this effect should be taken into account to reach an accurate, reliable and optimized design for Nano-switches.

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“…Different from the piezoelectricity existing only in the non-centrosymmetric materials, the flexoelectricity widely exists in all dielectric materials due to the strain gradient breaking the inversion symmetry of crystals. Therefore, the flexoelectricity provides potential opportunities for non-centrosymmetric materials in the applications of electromechanical systems (Chu et al, 2009;Jiang et al, 2013;Deng et al, 2014;Bhaskar et al, 2016;Zhang et al, 2017;Baroudi et al, 2018). However, the flexoelectric effect is relatively weak in bulk materials compared with the piezoelectric effect, it received little attention in past decades.…”

Section: Introductionmentioning

confidence: 99%