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A liquid inclusion having an n-fold axis of symmetry in an infinite isotropic elastic matrix

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Abstract

We first study the plane strain problem associated with an incompressible liquid inclusion having an n-fold axis of symmetry which is embedded in an infinite isotropic elastic matrix subjected to uniform remote hydrostatic stresses. A closed-form solution is derived using Muskhelishvili’s complex variable formulation, a four-term conformal mapping function and the application of analytic continuation. The pair of analytic functions characterizing the elastic field in the matrix is completely determined in elementary closed-form. Explicit expressions are obtained and graphically illustrated for the internal uniform hydrostatic stresses within the liquid inclusion and the hoop stress along the liquid–solid interface on the matrix side. The closed-form solution for a linearly compressible liquid inclusion having an n-fold axis of symmetry is also obtained.

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Acknowledgements

The authors are grateful to two reviewers for their very helpful comments and suggestions. In particular, we are grateful to one reviewer for suggesting that we compare our result with the formula for the determination of the Skempton’s induced pore-pressure coefficient by Zimmerman [16]. This work is supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN-2023-03227 Schiavo).

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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

  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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Correspondence to Xu Wang or Peter Schiavone.

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Wang, X., Schiavone, P. A liquid inclusion having an n-fold axis of symmetry in an infinite isotropic elastic matrix. Continuum Mech. Thermodyn. 36, 229–239 (2024). https://doi.org/10.1007/s00161-023-01274-0

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