Dependence of Young׳s modulus of nanowires on surface effect

Static bending of nanowires based on the Timoshenko beam theory incorporating a surface effect is investigated. Analytic expressions for the transverse deflection of bending of a nanowire subjected to a concentrated force are obtained. In particular, force–displacement relations are derived for three typical cases: cantilevered, simply supported and clamped nanowires. The influences of residual surface tension and surface elasticity on the transverse deflection are discussed. The obtained results indicate that positive surface stresses increase the deflection of cantilever nanowires and negative ones decrease the deflection. For simply supported and clamped nanowires, the trend is completely opposite. Consideration of the residual surface tension causes the nanowire to become stiffer or softer depending on the end constraint. Effective Young׳s modulus of nanowires depends on the diameter and length, and the size effects of elastic properties of nanowires are mainly due to surface stiffening or softening.