Effects of high-order surface stress on buckling and resonance behavior of nanowires

A theoretical framework, accounting for high-order surface stress, is implemented in a continuum mechanics model based on the Euler-Bernoulli theory of beams and columns to simulate the buckling and resonance behavior of nanowires (NWs). Closed-form expressions for the critical buckling load of uniaxial compression of NWs are derived for different types of end conditions. Size-dependent overall Young's modulus is characterized versus the diameter of the NWs and is compared with the experimental data. The resonance frequency of NWs is also studied and compared with the simulation results based on nonlinear, finite deformation kinematics. We demonstrate that the present prediction considering both surface moment and surface stress agrees well with the experimental data, while the pure surface stress model may not be able to capture the general trend when the NW's diameter is less than a certain size. We conclude that the present continuum mechanics approach, considering both high-order surface effects, could be served as one of the feasible tools to analyze the mechanical behavior of nanostructures.