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

Abstract

The 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.