Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids

Chen, Tungyang; Chiu, Min Sen; Weng, Chung Ning

doi:10.1063/1.2356094

Cited by 336 publications

(163 citation statements)

References 25 publications

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“…where, ∇ s is the surface gradient operator [24,25,30]. When the surface stress is isotropic, Υ = ΥI 2 , where I 2 is the 2D identity tensor, this boundary condition simplifies to…”

Section: A Surface Stress As a Boundary Condition At An Interfacementioning

confidence: 99%

Elastocapillarity: Surface Tension and the Mechanics of Soft Solids

Style

Jagota

Hui

et al. 2017

Annu. Rev. Condens. Matter Phys.

318

282

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It is widely appreciated that surface tension can dominate the behavior of liquids at small scales. Solids also have surface stresses of a similar magnitude, but they are usually overlooked. However, recent work has shown that these can play an central role in the mechanics of soft solids such as gels. Here, we review this emerging field. We outline the theory of surface stresses, from both mechanical and thermodynamic perspectives, emphasizing the relationship between surface stress and surface energy. We describe a wide range of phenomena at interfaces and contact lines where surface stresses play an important role. We highlight how surface stresses causes dramatic departures from classic theories for wetting (Young-Dupré), adhesion (Johnson-Kendall-Roberts), and composites (Eshelby). A common thread is the importance of the ratio of surface stress to an elastic modulus, which defines a length scale below which surface stresses can dominate.

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“…where, ∇ s is the surface gradient operator [24,25,30]. When the surface stress is isotropic, Υ = ΥI 2 , where I 2 is the 2D identity tensor, this boundary condition simplifies to…”

Section: A Surface Stress As a Boundary Condition At An Interfacementioning

confidence: 99%

Elastocapillarity: Surface Tension and the Mechanics of Soft Solids

Style

Jagota

Hui

et al. 2017

Annu. Rev. Condens. Matter Phys.

318

282

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“…According to the generalized Young-Laplace equations (Chen et al 2006b), these traction jumps T x , T y and T z with the consideration of plate deformation can be expressed as …”

Section: Formulationmentioning

confidence: 99%

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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“…Using force balance considerations, the derivation of the surface boundary conditions leads to generalized Young-Laplace equations where some components of the bulk stress tensor σ are now related to σ S and the curvature of the surface. 26 In the present case of an infinite circular nanowire of radius R, the surface boundary conditions for the cylindrical coordinate system (r,θ ,z) write…”

Section: B Bulk and Surface Propertiesmentioning

confidence: 99%

“…These questions have received lots of attention during these last decades since the pioneering mathematical works of Gurtin and Murdoch. [23][24][25] Using, for instance, the Chen et al 26 approach, the surface stress is described as symmetric 2×2 tensor σ S in the tangent plane of the curved surface. This latter is seen as a vanishingly thin membrane which can sustain in-plane stresses but offers no resistance for bending.…”

Section: B Bulk and Surface Propertiesmentioning

confidence: 99%

Displacement field of a screw dislocation in a〈011〉Cu nanowire: An atomistic study

Gailhanou

Roussel

2013

Phys. Rev. B

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By performing atomistic calculations with a tight-binding potential, we study the displacement field induced by a screw dislocation lying along a free 011 Cu cylindrical nanowire. For this anisotropic orientation that is often encountered experimentally, we show that the displacement field u z along the nanowire can be seen as the superposition of three different fields: the screw dislocation field in an infinite medium, the warping displacement field caused by the so-called Eshelby twist, and an additional image field induced by the free surfaces. A Fourier series analysis of this latter image displacement and stress fields is given. For a circular cross section of the wire, this image field corresponds mainly to an additional warping displacement u z ∝ xy. The dissociation mechanism of the dislocation into partials and the surface stress effects being also captured in our simulations, the present study enables one to quantify the various contributions to the formation of the x-ray diffractograms.

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Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids

Abstract: In nanoscaled solids, the mathematical behavior of a curved interface between two different phases with interface stress effects can be described by the generalized Young-Laplace equations ͓T. Young,

Cited by 336 publications

References 25 publications

Elastocapillarity: Surface Tension and the Mechanics of Soft Solids

Elastocapillarity: Surface Tension and the Mechanics of Soft Solids

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

Displacement field of a screw dislocation in a〈011〉Cu nanowire: An atomistic study

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