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Boussinesq problem with the surface effect based on surface energy density

机译：基于表面能密度的表面效应的Boussinesq问题

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摘要

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.
机译：表面效应在纳米化材料中起着重要作用。在本文中，基于陈瑶的表面弹性理论，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对材料的机械性能的表面影响。采用傅里叶积分变换方法来导出Boussinesq问题的接触应力和位移场。作为两个示例，详细分别通过均匀分布压力和浓缩力引起的变形。本文的理论结果表明，凹进的堆积底物的表面能密度仅作为一个附加参数，作为影响与经典接触模型相比的接触性能的重要因素。数值结果表明，当考虑表面效应时，半无限基板变硬。缩放分析进一步表明，仅当接触宽度与剪切模量的体积能密度的比率相等时，表面效应的理论预测与没有表面效果的经典接触溶液之间的差异是显着的。结果提供了对纳米材料的表面效应的进一步了解，这应该有助于设计和准确评估纳米材料或纳米材料的服务性能。

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