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

Author

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  • Alexander Khludnev

    (Lavrentyev Institute of Hydrodynamics of the RAS)

  • Alexander Rodionov

    (Saint-Petersburg State Marine Technical University)

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.

Suggested Citation

  • Alexander Khludnev & Alexander Rodionov, 2023. "Elasticity Tensor Identification in Elastic Body with Thin Inclusions: Non-coercive Case," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 993-1010, June.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02216-1
    DOI: 10.1007/s10957-023-02216-1
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    References listed on IDEAS

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    1. Alexander Khludnev & Antonio Corbo Esposito & Luisa Faella, 2020. "Optimal Control of Parameters for Elastic Body with Thin Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 184(1), pages 293-314, January.
    2. Alexander Khludnev, 2017. "Rigidity Parameter Identification for Thin Inclusions Located Inside Elastic Bodies," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 281-297, January.
    3. Nyurgun Lazarev & Galina Semenova, 2018. "An Optimal Size of a Rigid Thin Stiffener Reinforcing an Elastic Two-Dimensional Body on the Outer Edge," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 614-626, August.
    4. T. Durante & T. A. Mel’nyk, 2010. "Asymptotic Analysis of an Optimal Control Problem Involving a Thick Two-Level Junction with Alternate Type of Controls," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 205-225, February.
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    1. Alexander Khludnev & Antonio Corbo Esposito & Luisa Faella, 2020. "Optimal Control of Parameters for Elastic Body with Thin Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 184(1), pages 293-314, January.

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