Surface Effect on the Elastic Behavior of Static Bending Nanowires

Abstract

The surface effect from surface stress and surface elasticity on the elastic behavior of nanowires in static bending is incorporated into Euler-Bernoulli beam theory via the Young-Laplace equation. Explicit solutions are presented to study the dependence of the surface effect on the overall Young's modulus of nanowires for three different boundary conditions: cantilever, simply supported, and fixed-fixed. The solutions indicate that the cantilever nanowires behave as softer materials when deflected while the other structures behave like stiffer materials as the nanowire cross-sectional size decreases for positive surface stresses. These solutions agree with size dependent nanowire overall Young's moduli observed from static bending tests by other researchers. This study also discusses possible reasons for variations of nanowire overall Young's moduli observed.

Surface effect on resonant properties of nanowires predicted by an elastic theory for nanomaterials

“…1,[11][12][13][14][15] Size-dependently effective Young's modulus of nanowires has been achieved, which depends on the surface elastic modulus. 1,13 In addition, molecular dynamics (MD) simulation, as a major numerical approach, has also been adopted to study the size effect of nanowires' elastic properties.…”

“…The fundamental resonant frequency of both fixed-fixed nanowires and cantilevered ones exhibits the same varying trend as that of the effective elastic moduli. 12 Later, the Y-L model was extended to the vibration problem of Timoshenko nanowires. 36,37 Chiu and Chen 38 further discussed the effect of the surface bending modulus on the resonant frequency of nanowires.…”

“…40 in which surface elastic constants, including the surface elastic modulus and surface bending modulus, serve as critical parameters influencing the size-dependent behavior of nanowires. 12,13,31,35,38 However, surface elastic constants needed by the surface elasticity theory can only be provided by MD simulation and hardly be measured by proper experiment techniques. 1,13,41,42 How to define the atomic layer as a surface layer, how to choose a proper atomic interaction potential and the size of a numerical model are still open questions in MD simulation.…”

A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology

“…They demonstrated that surface effects become significant when at least one of the dimensions of the problem is in the nanometer range. The influence of the surface on the elastic behaviour of nanowires in static bending was investigated by He and Lilley (2008) using the Young-Laplace equation. Hung and Wang (2006); Wang et al (2010b) proposed a theory of hyperelasticity accounting for surface energy effects and showed how surface tension induces a residual stress field in the bulk of nanostructures.…”

Platinum composite nanowires for ultrasensitive mass detection

“…24,29 The reason for the significant higher values of Young's modulus of nanowires with smaller diameters is not yet entirely clear, although the surface properties and the micro-structure may play important roles, and there exists a strong size effect at the nanoscale scale. [30][31][32][33] It is known that in nanowires with tens of nanometer in diameter, the surface modulus 34 (that is determined by the surface state) is introduced, and the wires can be much more elastic 31 when compared with their bulk counterparts. With the decreasing diameter, surface effects are expected to be more significant.…”