Displacement Approach to Determine the Effective Tensile and Torsional Modulus of Nanowires

Surface elasticity and residual stress have a strong influence on the effective properties of nanowire (NW) due to its excessively large surface area-to-volume ratio. Here, the classical displacement method is used to solve the field equations of the core-surface layer model subjected to tension and torsion. The effective Young’s modulus is defined as the ratio of normal stress to axial strain, which decreases with the increase in NW radius and gradually reaches the bulk value. The positive or negative surface residual stresses will increase or decrease Young’s modulus and shear modulus due to the surface residual strains. Nonzero radial and circumferential strains enhance the influence of surface moduli on the effective modulus.