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.