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In-plane stress analysis of two nanoscale holes under surface tension

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Abstract

Studied in this paper is the surface tension-induced stress field around two nanoscale holes in an infinite, elastic matrix. The complex variable method is adopted to describe the assumed plane-strain deformation of the structure. The stress boundary conditions at the surfaces of the holes are formulated via the integral-type Gurtin–Murdoch model. The stress field is finally obtained with the aid of conformal mapping and series expansion methods. Numerical examples are demonstrated for the case of one approximately triangular, smooth hole and one approximately square, smooth hole. A detailed discussion is carried out about the influence of the distance between the two holes on the stress field.

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Acknowledgements

Wang appreciates the support of the China Scholarship Council. Yang thanks the support from the National Natural Science Foundation of China (11702147 and 11502090). Wang and Gao acknowledge the support of the National Natural Science Foundation of China (11472130). Chen thanks the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support.

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Authors and Affiliations

  1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Shuang Wang & Cunfa Gao

  2. Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada

    Shuang Wang & Zengtao Chen

  3. Department of Mechanics Engineering, School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510641, China

    Hai-Bing Yang

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  1. Shuang Wang
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Correspondence to Cunfa Gao or Zengtao Chen.

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Appendix

Appendix

Here we plot the stress distribution in the vicinity of the holes. Note that different from the stress distribution around the boundaries of the holes, which is plotted in the local \(\left( {n,\;t} \right) \) coordinate system, the stress distribution here is plotted in the global \(\left( {x,\;y} \right) \) coordinate system (See Figs. 5, 6, 7).

Fig. 5
figure 5

Distribution of the dimensionless stress \({\sigma _{x} R}/T\) around the triangular and square holes

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Fig. 6
figure 6

Distribution of the dimensionless stress \({\sigma _{y} R}/T\) around the triangular and square holes

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Fig. 7
figure 7

Distribution of the dimensionless stress \({\sigma _{xy} R}/T\) around the triangular and square holes

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Wang, S., Yang, HB., Gao, C. et al. In-plane stress analysis of two nanoscale holes under surface tension. Arch Appl Mech 90, 1363–1372 (2020). https://doi.org/10.1007/s00419-020-01672-9

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