Influence of surface roughness on the stress field around a nanosized hole with surface elasticity

  • Hai-Bing Yang
  • Ming DaiEmail author


Based on the complex variable techniques, the stress concentration around a nanosized hole with rough surface in an elastic plane under uniform remote in-plane loadings is studied in this paper. The hole is nearly circular with its surface asperities defined by a conformal mapping. The nanoscale effects on the stress field around the hole are described by the Gurtin–Murdoch model. Several numerical examples are presented to study the influence of the amplitude and period of the surface asperities on the stress field around the hole for a uniform remote uniaxial tensile loading. It is shown that for a given period of the surface asperities, the maximum normal, tangential and hoop stresses around the hole all increase significantly with increasing amplitude of the surface asperities. On the other hand, it is found that for a given amplitude of the surface asperities, when the period of the surface asperities decreases, the maximum normal and tangential stresses increase rapidly although the maximum hoop stress hardly changes.


Gurtin–Murdoch model Surface asperities Surface elasticity Complex variable Nanosized hole 

Mathematics Subject Classification

74B05 74E05 74G10 



This study was funded by the National Natural Science Foundation of China (Grant Number 11502090).

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mechanics Engineering, School of Civil Engineering and TransportationSouth China University of TechnologyGuangzhouChina
  2. 2.State Key Laboratory of Mechanics and Control of Mechanical StructuresNanjing University of Aeronautics and AstronauticsNanjingChina

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