Surface effect plays an important role in nanosized materials. In this paper, two-dimensional Boussinesq problem with the surface effect is systematically investigated based on Chen–Yao’s surface elastic theory, in which surface effect on mechanical properties of materials is considered based on the concept of surface energy density. The Fourier integral transform method is adopted to derive the contact stress and displacement fields of the Boussinesq problem. As two examples, the deformations induced, respectively, by a uniform distributed pressure and a concentrated force are analyzed in detail. The theoretical result in this paper show 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 results show that the semi-infinite substrate becomes hardened when the surface effect is considered. Scaling analysis further indicates 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. The results provide a further understanding of the surface effect of nanomaterials, which should be helpful for the design and accurate evaluation of service performance of nanoscale devices or nanomaterials.

表面效应在纳米材料中起着重要作用。本文基于Chen-Yao的表面弹性理论，系统地研究了具有表面效应的二维Boussinesq问题，其中基于表面能密度的概念考虑了表面对材料力学性能的影响。采用傅里叶积分变换法推导了Boussinesq问题的接触应力和位移场。作为两个例子，详细分析了分别由均匀分布的压力和集中力引起的变形。本文的理论结果表明，与传统的接触模型相比，凹入的块状衬底的表面能密度仅作为一个附加参数，是影响接触性能的重要因素。数值结果表明，当考虑表面效应时，半无限基底变硬。比例分析还表明，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值与没有表面效应的经典接触溶液之间的差异才是显着的。结果提供了对纳米材料表面效应的进一步理解，这将有助于设计和准确评估纳米级器件或纳米材料的服务性能。比例分析还表明，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值与没有表面效应的经典接触溶液之间的差异才是显着的。结果提供了对纳米材料表面效应的进一步理解，这将有助于设计和准确评估纳米级器件或纳米材料的服务性能。比例分析还表明，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值与没有表面效应的经典接触溶液之间的差异才是显着的。结果提供了对纳米材料表面效应的进一步理解，这将有助于设计和准确评估纳米级器件或纳米材料的服务性能。