In this paper, the two-dimensional nano-contact problem with the surface effect is systematically investigated based on Chen–Yao’s surface elastic theory. The Fourier integral transform method is adopted to derive the contact stress and displacement fields of a half-space subjected to a normal triangle distribution force. The theoretical result shows that the surface energy density of the indented bulk substrate, as only one additional parameter, serves as an important factor to influence the contact properties in contrast to the classical contact models. The numerical show that only when the ratio of the contact width to the volume surface energy density to the shear modulus is equal, the difference between the theoretical prediction of surface effect and the classical contact solution without surface effect will be significant. This result indicates that when the surface effect is considered and the surface effect parameter is positive, the semi-infinite substrate will harden, which should be helpful for better understanding the size-dependent mechanisms of surface energy density at nanoscale.

本文基于陈耀的表面弹性理论系统地研究了具有表面效应的二维纳米接触问题。采用傅里叶积分变换方法推导出正三角形分布力作用下半空间的接触应力和位移场。理论结果表明，与经典接触模型相比，凹痕体衬底的表面能密度作为一个附加参数，是影响接触特性的重要因素。数值表明，只有当接触宽度与体积表面能密度与剪切模量的比值相等时，表面效应的理论预测与没有表面效应的经典接触解的差异才会显着。