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Design of a neutral elastic inhomogeneity via thermal expansion

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Abstract

A neutral elastic inhomogeneity does not affect the existing stress field when inserted into an elastic body. It has been shown that no such inhomogeneity can exist under the classical assumption of a perfectly bonded interface between the inhomogeneity and the surrounding material. We show that by introducing a suitable temperature field inside the inhomogeneity it is indeed possible to achieve neutrality regardless of the perfect bonding assumption. Specifically, we show that a nonuniform internal temperature field can induce neutrality in an inhomogeneity in the form of an elastic ring with concentric internal and external boundaries of arbitrary shape. Noting that such a temperature field can be identified also in the case of an unpunched inhomogeneity when the inhomogeneity is line-shaped, we further prove that even a flake-shaped inhomogeneity can be made neutral if the thickness of the flake is much smaller than its length. In the case that the elastic body surrounding the unpunched inhomogeneity is subjected to remote hydrostatic loading, the temperature field within the inhomogeneity will remain uniform and independent of the shape of the inhomogeneity. In fact, in this case, the temperature field inside the inhomogeneity depends only on the elastic parameters of the composite and the direction of the remote loading and can be higher or lower than the operating temperature of the composite.

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Acknowledgements

The authors are indebted to one particular anonymous reviewer whose comments and constructive criticisms have greatly improved the paper. K. Song appreciates the support of the China Scholarship Council. H.P. Song and Gao acknowledge the support of the National Natural Science Foundation of China (Grant Nos. 11872203 and 11202099), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). Schiavone thanks the Natural Sciences and Engineering Research Council of Canada for their support by a Discovery Grant (Grant # RGPIN 155112).

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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, People’s Republic of China

    H. P. Song & C. F. Gao

  2. College of mechanics and materials, Hohai University, No. 8 Fochengxi Road, Jiangning District, Nanjing, 211100, Jiangsu, People’s Republic of China

    H. P. Song & K. Song

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

    P. Schiavone

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  1. H. P. Song
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  2. K. Song
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  3. P. Schiavone
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  4. C. F. Gao
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Correspondence to P. Schiavone or C. F. Gao.

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Song, H.P., Song, K., Schiavone, P. et al. Design of a neutral elastic inhomogeneity via thermal expansion. Acta Mech 231, 2867–2876 (2020). https://doi.org/10.1007/s00707-020-02677-9

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  • DOI: https://doi.org/10.1007/s00707-020-02677-9

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