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Uniformity of stresses inside a non-elliptical inhomogeneity interacting with a circular Eshelby inclusion in anti-plane shear

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Abstract

We use conformal mapping techniques to examine the uniformity of stresses inside a non-elliptical inhomogeneity interacting with a circular Eshelby inclusion in an elastic matrix subjected to remote uniform stresses in anti-plane shear. We show that for a prescribed set of two real loading and two complex geometric parameters, it is possible to determine the single unknown complex coefficient in the mapping function and the (unique) shape of the corresponding inhomogeneity enclosing internal uniform stresses. Our results indicate that the shape of the inhomogeneity depends on the circular Eshelby inclusion whereas the uniform stress field inside the inhomogeneity does not. Finally, we note that the influence of the circular Eshelby inclusion in the vicinity of the inhomogeneity allows for the possibility of a sharp corner on the boundary of the inhomogeneity.

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Acknowledgements

The authors are indebted to two reviewers for their very helpful comments and suggestions. This work is supported by the National Natural Science Foundation of China (Grant No. 11272121) and through a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN – 2017 - 03716115112).

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, China

    Xu Wang & Liang Chen

  2. Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, AB, T6G 1H9, Canada

    Peter Schiavone

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  1. Xu Wang
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  2. Liang Chen
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  3. Peter Schiavone
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Correspondence to Xu Wang or Peter Schiavone.

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Wang, X., Chen, L. & Schiavone, P. Uniformity of stresses inside a non-elliptical inhomogeneity interacting with a circular Eshelby inclusion in anti-plane shear. Arch Appl Mech 88, 1759–1766 (2018). https://doi.org/10.1007/s00419-018-1401-y

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  • DOI: https://doi.org/10.1007/s00419-018-1401-y

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