A continuum model for the mechanical behavior of nanowires including surface and surface-induced initial stresses

Abstract

a b s t r a c tThe continuum modeling of the mechanical behavior of nanowires has recently attracted much attention due to its simplicity and efficiency. However, there are still some critical issues to be solved. In this paper, we demonstrate the importance of accounting for the effects of initial stresses in the nanowires that are caused by deformation due to surface stresses; we note that such initial stresses have previously been neglected in most existing continuum models. By considering the local geometrical nonlinearity of strains during the incremental flexural motion, a new formulation of the Euler-Bernoulli beam model for nanowires is developed through the incremental deformation theory, in which effects of the surface stress, the surface-induced initial stress and surface elasticity are naturally incorporated. It is found through comparisons to existing experimental and computational results for both fcc metal and ceramic nanowires that the surface-induced initial stresses, which are neglected in the Young-Laplace model, can significantly influence the overall mechanical properties of nanowires. We additionally demonstrate and quantify the errors induced by using the Young-Laplace model due to its approximation of surface stresses acting on only the top and bottom surfaces of nanowires.

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

“…In the following research, only the smallest positive solution of the two equations is numerically solved, which is referred as the angular resonant frequency for the first vibration modes (fundamental resonant frequency). 35,58 Meanwhile, according to the conventional structural dynamics, 59 the fundamental frequency for a bulk solid is,…”

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

“…It should be mentioned that such in-plane relaxation strains of elastic nanowires owing to the surface stresses have been discussed in the literature by using atomistic or atomistic-based theories (Park & Klein 2007;Zhang et al 2010b;Park 2012). In addition, by considering a relaxation process before bending deformation, Song et al (2011) studied the mechanical behaviour of nanowires by using a continuum model. 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.…”

Determining the effects of surface elasticity and surface stress by measuring the shifts of resonant frequencies

“…The second condition, in other words, is to say that the in-plane distributed load induced by the side surfaces can be ignored. Song et al [28] shifts of the beam resonant frequencies. Therefore, the method can be applied to the concentrated load model and modified YL models alike.…”

“…We see that ∂ 2 w/∂x 2 is the curvature of the upper/lower surface and F is in the horizontal direction; −F∂ 2 w/∂x 2 is a distributed transverse load given by the Young-Laplace (YL) formula [38]. Therefore, the concentrated load model of equation (2.1) is also referred to as the YL model [28,31]. Here, positive F is tensile and negative is compressive.…”

“…Similarly, Chiu & Chen [30] derived an analytical expression for the buckling load of a nanowire, which indicates that the surface stress contribution to the buckling load is also amplified by a factor of (L/D) 2 compared with that of surface elasticity. It is also necessary to bear in mind that in the modified YL models [28,31], the transverse surface stress and surface stress from side surfaces can significantly enhance the effective surface elasticity effect by increasing the nanowire bending stiffness. It is noted that C s and σ calculated by atomistic simulation can be significantly different for the same material.…”