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.

中文翻译：

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确定纳米线有效拉伸和扭转模量的位移方法

由于纳米线 (NW) 的表面积与体积比过大，表面弹性和残余应力对纳米线的有效性能有很大影响。在此，采用经典位移法求解受张力和扭转作用的芯-表层模型的场方程。有效杨氏模量定义为法向应力与轴向应变的比值，随着 NW 半径的增加而减小并逐渐达到体积值。由于表面残余应变，正或负表面残余应力将增加或减少杨氏模量和剪切模量。非零径向和周向应变增强了表面模量对有效模量的影响。