Timoshenko beam model for static bending of nanowires with surface effects

In this paper, surface effects on the elastic behavior of static bending nanowires (NWs) are studied by using a comprehensive Timoshenko beam model. For NWs with different boundary conditions, explicit solutions are derived to study the combined effects of residual surface stress, surface elasticity and shear deformation on the effective stiffness and Young's modulus of the NWs. The stiffness is found to be size-dependent and this dependence is more significant for slender NWs. Residual surface stress tends to increase or decrease the stiffness of NWs depending on their boundary conditions, and the shear deformation always makes the NWs softer compared with the results of the Euler–Bernoulli beam model. The solutions agree well with experimental measurement in predicting the Young's modulus, especially for NWs with small length-to-thickness ratio. This work might be helpful for characterizing the mechanical properties of NWs and the design of nanobeam-based devices.