Effects of high-order surface stress on static bending behavior of nanowires

Studies on surface effects in nano-sized materials or structures are often based on the framework of linear membrane theory, in which the field jumps at the interface are characterized by the generalized YoungLaplace equation. Here a recently proposed theoretical framework of high-order surface stress is implemented in a continuum mechanics model to simulate the bending behavior of nanowires. The high-order surface stress considers not only the effect of in-plane membrane surface stresses, but also the surface moments induced from the non-uniform surface stress across the layer thickness. We investigate the extent to which the high-order surface stress will influence the bending behavior of nanowires deviated from that predicted by the generalized YoungLaplace equation. Closed-form expressions for the deflection curves are derived for nanowires with different boundary conditions. These solutions are utilized to characterize the size-dependent overall Youngs moduli of NWs. We demonstrate that, in comparison to the reported experimental data, the present framework provides more accurate results than those by the conventional surface stress model. This study might be helpful to accurately characterize the behavior of bending nanowires in a wide range of applications.