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Integral-Type Stress Boundary Condition in the Complete Gurtin-Murdoch Surface Model with Accompanying Complex Variable Representation

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Abstract

In the large majority of papers utilizing the Gurtin-Murdoch (G-M) model of a material surface, the complete model is avoided in favor of various modified versions often because they lead to simpler representations of the corresponding stress boundary condition. We propose in this paper an integral-type stress boundary condition for the plane deformations of a bulk-interface composite system which allows for an equally simple implementation of the complete G-M model. Since the mechanical behavior of such composite systems is often analyzed using complex variable methods, we formulate our ideas accordingly, in this context. Remarkably, in contrast to what is often believed to be the case, we find that boundary value problems based on our formulation of the stress boundary condition offer no added difficulty when utilizing the complete G-M model versus its various simplified counterparts. This new representation of the stress boundary condition is concise in form and will prove to be extremely useful in, for example, the calculation of the elastic field in the vicinity of nano-inhomogeneities of irregular shape.

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Acknowledgements

Wang thanks the National Natural Science Foundation of China (Grant No.: 11702147). Schiavone thanks the Natural Sciences and Engineering Research Council of Canada for their support through a Discovery Grant (Grant No.: RGPIN-2017-03716115112).

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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

    Ming Dai

  2. School of Mechanical Engineering, Changzhou University, Changzhou, 213164, China

    Ming Dai

  3. College of Engineering, Nanjing Agricultural University, Nanjing, 210031, China

    Yong-Jian Wang

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

    Peter Schiavone

Authors
  1. Ming Dai
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  2. Yong-Jian Wang
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  3. Peter Schiavone
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Correspondence to Peter Schiavone.

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Dai, M., Wang, YJ. & Schiavone, P. Integral-Type Stress Boundary Condition in the Complete Gurtin-Murdoch Surface Model with Accompanying Complex Variable Representation. J Elast 134, 235–241 (2019). https://doi.org/10.1007/s10659-018-9695-0

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  • DOI: https://doi.org/10.1007/s10659-018-9695-0

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