Surface effects in various bending-based test methods for measuring the elastic property of nanowires

The size-dependent elastic property of nanowires induced by the surface effect is investigated by using the core-shell model. The overall effective elastic moduli of nanowires with regular polygonal cross-sections are unified into a simple and explicit relation. It is found that the effect of surface elasticity on the elastic moduli can be well characterized by two dimensionless material and geometric parameters with clear physical meaning. Finite element simulations demonstrate that the derived theoretical relation is applicable for all the vibration, bending, and buckling test methods for measuring the mechanical properties of nanowires. The analytical result is also validated by comparing it with relevant experimental measurements. This study is helpful not only for interpreting various phenomena associated with size-dependent mechanical properties of nanowires but also for developing and evaluating test techniques for material characterization at the nanoscale.