Effect of surface elasticity on extensional and torsional stiffnesses of isotropic circular nanorods

Abstract

We present a continuum formulation to obtain the effects of surface residual stress and surface elastic constants on extensional and torsional stiffnesses of isotropic circular nanorods. Analytical expressions of axial force, twisting moment, and extensional and torsional stiffnesses are obtained. Unlike the case of rectangular nanorods, we show that the stiffnesses of circular nanorods also depend on surface residual stress components. This is attributed to non-zero surface curvature inherent in circular nanorods. We further normalize these expressions and analyze their asymptotic limits in the limit of the nanorod’s radius approaching both zero and infinity, corresponding to surface-dominated and bulk-dominated regimes, respectively. Finally, we use the recently proposed helical Cauchy–Born rule and perform molecular statics calculations to obtain axial force, twisting moment, and stiffnesses of the tungsten nanorod. The tungsten material is selected since its bulk crystal exhibits isotropy in the stress-free state. The results from molecular statics calculations are shown to match the derived continuum formulas accurately.

Atomistic to continuum model for studying mechanical properties of RNA nanotubes

“…stress and strain, of RNA nanotubes. We approach the modeling strategy of RNA nanotubes based on the ideas similar to the modeling of carbon nanotubes and several other nanorods (Cheng et al 2009b;Tserpes and Papanikos 2005;Odijk 1986;Kohji et al 1978;Tashiro et al 1978;Badu and Melnik 2017b;Fatehiboroujeni et al 2018;Fang et al 2013;Gupta and Kumar 2018;Fatehiboroujeni et al 2018;Maghsoodi and Perkins 2018;Kumar et al 2016;Schmidt et al 2015;Gupta and Kumar 2017;Venkataiah et al 2018;Badu and Melnik 2017a).…”

Effect of Curvature‐Dependent Surface Elasticity on the Flexural Properties of Nanowire

“…Notably, the difference in surface residual stress on the upper and lower surfaces induces the relaxation curvature of nanowire. If Δτ s0 � 0, that is, τ su0 � τ sl0 , then equation (12) shows that κ y0 � 0, and no bending deformation emerges in the relaxed state. e height of neutral axis h y0 has no meaning in such a case.…”

“…e definition of surface parameters depends on the constitutive relationship of nanowire, which is obscure in surface/interface mechanics. e hyperelastic model is the most commonly used constitutive model in which the surface energy density can be expressed by a function of the invariants of surface strain and relative curvature tensors [9,12]. e derived relationship among surface stress, surface strain, and curvature denotes the usual nonlinear elasticity.…”

“…Circular nanowire with no external load may also present surface residual and couple stresses due to the initial curvature. e extensional properties of circular nanowire have been discussed in detail in [12,13]. Rectangular nanowire represents different mechanisms on the surface from the circular nanowire.…”

Displacement Approach to Determine the Effective Tensile and Torsional Modulus of Nanowires

“…Typical nanowires (NWs) are often referred to as 1D materials with nanometer-scale diameters or perimeters and excessively large surface area-to-volume ratio. NWs have considerable potential in various applications, such as molecular electronics, nanoelectromechanical systems, and novel building materials, for disaster prevention and mitigation [1][2][3][4][5][6][7][8][9][10][11][12]. e applications of NWs into future generation nanodevices require a complete understanding of the NW mechanical properties [2].…”