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Green’s functions for an anisotropic elastic matrix containing an elliptical incompressible liquid inclusion

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Abstract

We use the Stroh sextic formalism for anisotropic elasticity and Muskhelishvili’s complex variable formulation for isotropic elasticity to derive a full-field closed-form solution to the generalized plane strain problem of an elliptical incompressible liquid inclusion embedded in an infinite anisotropic elastic matrix subjected to a line force and a line dislocation. An explicit expression for the internal uniform hydrostatic tension within the liquid inclusion is obtained. Furthermore, in the case when the line force and line dislocation approach the elliptical liquid–solid interface, we develop a real-form solution for the internal uniform hydrostatic tension in terms of the Barnett–Lothe tensors for the matrix.

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Acknowledgements

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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  2. Peter Schiavone
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Correspondence to Xu Wang or Peter Schiavone.

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Wang, X., Schiavone, P. Green’s functions for an anisotropic elastic matrix containing an elliptical incompressible liquid inclusion. Z. Angew. Math. Phys. 75, 27 (2024). https://doi.org/10.1007/s00033-023-02154-y

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