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A Nanoscale Hole of Arbitrary Shape with Surface Elasticity

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Abstract

In this paper, we study the plane deformation of an arbitrarily-shaped nanoscale hole subjected to a uniform mechanical load at the infinity. Stress boundary condition along the hole surface is constructed by incorporating the deformation-dependent surface elasticity. The solution is given via the complex variable techniques, including the conformal mapping and series expansion methods. To verify the present formulation, we compare our results for the elliptical holes with those from the literature and observe good agreement between the two sets of results. Then we present numerical examples for four shapes of holes (ellipse, square, pentagon and triangle) with varying sizes to investigate the stress field with surface elasticity. The first aspect we are interested in is what factors can affect the stress field. Our results show that for nanoscale holes with surface elasticity, the stress field can be greatly influenced by the hole size and the hole shape. Specifically, when the hole size decreases, the hoop stress usually decreases, while the normal and shear stresses always increase. However, the hole size hardly influences the stress distribution pattern, which is, in fact, determined by the hole shape. In addition, the hole shape strongly influences the stress magnitude. Another aspect concerned is the positions of the maximum stresses. The results show that for the most cases, the stresses obtain their maximums at a certain corner of the shapes. However, for some shapes, there might be certain stresses that attain their maximums nearby, not at, the corner of the shapes.

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Acknowledgements

Wang appreciates the support of the China Scholarship Council. 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 the 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 Mechanical Engineering, Tongling University, Tongling, 244061, China

    Shichao Xing

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  1. Shuang Wang
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  2. Shichao Xing
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  4. Cunfa Gao
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Correspondence to Zengtao Chen or Cunfa Gao.

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Wang, S., Xing, S., Chen, Z. et al. A Nanoscale Hole of Arbitrary Shape with Surface Elasticity. J Elast 136, 123–135 (2019). https://doi.org/10.1007/s10659-018-9700-7

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  • DOI: https://doi.org/10.1007/s10659-018-9700-7

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