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
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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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