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Eshelby’s inclusion problem in large deformations

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Abstract

In this contribution, we propose a multiplicative decomposition of the deformation gradient corresponding to the imagined procedure that Eshelby (Proc R Soc Ser A 241:376–396, 1957) used to investigate the theory of inclusions in the case of infinitesimal deformations. The proposed multiplicative decomposition is inspired by classical multiplicative decompositions reported in the literature and encompasses, as particular cases, other decompositions proposed for Eshelby’s inclusion problem. The linearisation of the proposed multiplicative decomposition coincides with the additive decomposition of the infinitesimal strain in Eshelby’s original procedure.

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Acknowledgements

Prof. Marcelo Epstein (University of Calgary) is gratefully acknowledged for crucial discussions about some differential geometric details of the work. Grazie, Marcelo. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, through the NSERC Discovery Programme, Grant Number RGPIN-2015-06027 [SF], and the Libyan Ministry of Education [MFA].

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  1. Department of Mechanical and Manufacturing Engineering, The University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada

    Mawafag F. Alhasadi & Salvatore Federico

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  1. Mawafag F. Alhasadi
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  2. Salvatore Federico
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Correspondence to Salvatore Federico.

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Alhasadi, M.F., Federico, S. Eshelby’s inclusion problem in large deformations. Z. Angew. Math. Phys. 72, 182 (2021). https://doi.org/10.1007/s00033-021-01594-8

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  • DOI: https://doi.org/10.1007/s00033-021-01594-8

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