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Elasticity Tensor Identification in Elastic Body with Thin Inclusions: Non-coercive Case

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Abstract

In the paper, we analyze problems of elasticity tensor identification for an elastic body with incorporated thin elastic and rigid inclusions in a non-coercive case. The inclusions are assumed to be delaminated from the surrounding elastic body, thus forming interfacial cracks. We consider inequality-type boundary conditions at the crack faces with unknown set of a contact to provide a mutual non-penetration between the crack faces. The considered problems are characterized by unknown displacement field and elasticity tensor. A formulation of identification problems includes an additional information, which can be found from a measurement. A solution existence of these problems is proved.

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Acknowledgements

The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation as part of World-class Research Center program: Advanced Digital Technologies (contract No. 075-15-2020-903 dated 16 November 2020).

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Authors and Affiliations

  1. Lavrentyev Institute of Hydrodynamics of the RAS, Novosibirsk, Russia, 630090

    Alexander Khludnev

  2. Saint-Petersburg State Marine Technical University, Saint Petersburg, Russia, 190121

    Alexander Rodionov

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  1. Alexander Khludnev
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  2. Alexander Rodionov
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Correspondence to Alexander Khludnev.

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Communicated by Christiane Tammer.

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Khludnev, A., Rodionov, A. Elasticity Tensor Identification in Elastic Body with Thin Inclusions: Non-coercive Case. J Optim Theory Appl 197, 993–1010 (2023). https://doi.org/10.1007/s10957-023-02216-1

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