Size-dependent nonlinear response of thin elastic films with nano-scale thickness

Lim, C.W.; He, Linghui

doi:10.1016/j.ijmecsci.2004.09.003

Cited by 219 publications

(103 citation statements)

References 15 publications

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“…However, this relaxation was not considered in the previous studies on the elastic nanoplate (Lim & He 2004;Lu et al 2006;) using modified continuum mechanics models, while atomistic or atomistic-based studies have confirmed and discussed this phenomenon (Park & Klein 2007;Zhang et al 2010b;Park 2012). 2. u 0 (x, y) = v 0 (x, y) = 0.…”

Section: Formulationmentioning

confidence: 99%

“…The results in these studies suggest that accounting for axial strain relaxation may be necessary to improve the accuracy and predictive capability of analytical surface elastic theories. However, this surface-stress-induced relaxation phenomenon has not been accounted for in previous investigations of nanoplates with surface effects (Lim & He 2004;Lu et al 2006;, owing to their particular prescribed in-plane boundary conditions. Therefore, different in-plane constraints will be defined in this work in order to catch all the possible phenomena induced by the surface effects.…”

Section: Introductionmentioning

confidence: 99%

“…In addition to the studies on the static and dynamic behaviours of nanobeams (Wang & Feng 2007He & Lilley 2008a,b;Liu & Rajapakse 2010), this surface elasticity model has also been adopted for modelling the elastic nanoplates. For example, Lim & He (2004) investigated surface effects on the large deflection of an ultra-thin film using von Karman plate theory. Lu et al (2006) used modified Kirchoff and Mindlin plate models to characterize the bending, vibration and buckling behaviour of nanoscale plates with surface effects.…”

Section: Introductionmentioning

confidence: 99%

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Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

2012

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This work investigates the surface effects on the vibration and buckling behaviour of a simply supported piezoelectric nanoplate (PNP) by using a modified Kirchhoff plate model. Two kinds of in-plane constraints are defined for the PNP, and the surface effects are accounted in the modified plate theory through the surface piezoelectricity model and the generalized Young-Laplace equations. Simulation results show that the influence of surface effects on the plate resonant frequency depends on the in-plane constraints significantly. For the PNP with different in-plane constraints, the effects of the applied electric potential, the mode number, the plate aspect ratio and the plate thickness on the resonant frequency are examined with consideration of the surface effects. The possible mechanical buckling of the PNP is also studied, and it is found that the surface effects on the critical electric voltage for buckling are sensitive to the plate thickness and aspect ratio. Our results also reveal that there exists a critical transition point at which the combined surface effects on the critical electric voltage may vanish under certain conditions.

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Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

2012

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“…9. In the following simulation, the nondimensional strain-independent surface stress parameter is introduced by (Lim & He, 2004). However, by considering the surface stress effects in the current model, we can find that the phase wave velocity increases with decrease of the size of the nanowire under surface tension.…”

Section: Flexural Wave Motionmentioning

confidence: 92%

Wave Propagation in Elastic Media with Micro/Nano-Structures

Huang¹,

Song²

2010

Wave Propagation in Materials for Modern Applications

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“…A general model for elastically isotropic solids with surface stress was suggested by [Gurtin and Murdoch 1975a;1975b;1978]. This model was adopted recently by some authors to analyze the elastic responses of nanoscale thin films [Lim and He 2004;Lu et al 2006]. We especially focus on the investigation of the thermomechanical properties in thin film with a thickness ranging from a few nanometers to several tens of nanometers, and the finite element method (FEM) for the thin film structure is also implemented based on the continuum model.…”

Section: Studiedmentioning

confidence: 99%

Multiscale analysis of nanoscale thin film considering surface effects: Thermomechanical properties

Choi

Cho

Kim

2010

JOMMS

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The classical model for a thin film, based on continuum theory, is independent of size, and ignores surface effects. But the surface-to-bulk ratio becomes very large in small-scale structures such as nanofilms, nanowires, and nanobeams, and surface effects play an important role. Molecular dynamics simulation has been a conventional way to analyze these ultrathin structures, but structures in the range between submicro and micro are difficult to analyze by molecular dynamics simulation due to the restrictions of computing resources and time. In the present study, a continuum-based, size-dependent model is developed for predicting the thermomechanical properties of nanoscale structures, especially thin films. The proposed continuum-based thin plate finite element is efficient and reliable for the prediction of nanoscale film behavior.

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Size-dependent nonlinear response of thin elastic films with nano-scale thickness

Cited by 219 publications

References 15 publications

Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

Wave Propagation in Elastic Media with Micro/Nano-Structures

Multiscale analysis of nanoscale thin film considering surface effects: Thermomechanical properties

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