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T-shape inclusion in elastic body with a damage parameter. / Khludnev, Alexander.

In: Journal of Computational and Applied Mathematics, Vol. 393, 113540, 09.2021.

Research output: Contribution to journal › Article › peer-review

Harvard

Khludnev, A 2021, 'T-shape inclusion in elastic body with a damage parameter', Journal of Computational and Applied Mathematics, vol. 393, 113540. https://doi.org/10.1016/j.cam.2021.113540

APA

Khludnev, A. (2021). T-shape inclusion in elastic body with a damage parameter. Journal of Computational and Applied Mathematics, 393, [113540]. https://doi.org/10.1016/j.cam.2021.113540

Vancouver

Khludnev A. T-shape inclusion in elastic body with a damage parameter. Journal of Computational and Applied Mathematics. 2021 Sept;393:113540. doi: 10.1016/j.cam.2021.113540

Author

Khludnev, Alexander. / T-shape inclusion in elastic body with a damage parameter. In: Journal of Computational and Applied Mathematics. 2021 ; Vol. 393.

BibTeX

@article{7e014f29119840078952ef2608116fb2,
title = "T-shape inclusion in elastic body with a damage parameter",
abstract = "We consider an equilibrium problem for a 2D elastic body with a thin elastic T-shape inclusion. A part of the inclusion is delaminated from the elastic body forming a crack between the inclusion and the surrounding elastic body. Inequality type boundary conditions are imposed at the crack faces preventing interpenetration between the crack faces. The model is characterized by a damage parameter. This parameter is responsible for connection at the junction points between different parts of the considered structure. Dependence of solutions on the damage parameter is investigated, in particular, a passage to infinity and to zero is analyzed. Inverse problems are considered provided that the damage parameter and Lam{\'e} parameters of the elastic body are unknown. In this case, a displacement of the tip point of the inclusion is assumed to be known. A solution existence of the inverse problems is proved.",
keywords = "Crack, Elastic body, Inverse problem, Non-penetration condition, T-shape inclusion, Variational inequality",
author = "Alexander Khludnev",
note = "Funding Information: The work is supported by Mathematical Center in Akademgorodok, Russia under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = sep,
doi = "10.1016/j.cam.2021.113540",
language = "English",
volume = "393",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - T-shape inclusion in elastic body with a damage parameter

AU - Khludnev, Alexander

N1 - Funding Information: The work is supported by Mathematical Center in Akademgorodok, Russia under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/9

Y1 - 2021/9

N2 - We consider an equilibrium problem for a 2D elastic body with a thin elastic T-shape inclusion. A part of the inclusion is delaminated from the elastic body forming a crack between the inclusion and the surrounding elastic body. Inequality type boundary conditions are imposed at the crack faces preventing interpenetration between the crack faces. The model is characterized by a damage parameter. This parameter is responsible for connection at the junction points between different parts of the considered structure. Dependence of solutions on the damage parameter is investigated, in particular, a passage to infinity and to zero is analyzed. Inverse problems are considered provided that the damage parameter and Lamé parameters of the elastic body are unknown. In this case, a displacement of the tip point of the inclusion is assumed to be known. A solution existence of the inverse problems is proved.

AB - We consider an equilibrium problem for a 2D elastic body with a thin elastic T-shape inclusion. A part of the inclusion is delaminated from the elastic body forming a crack between the inclusion and the surrounding elastic body. Inequality type boundary conditions are imposed at the crack faces preventing interpenetration between the crack faces. The model is characterized by a damage parameter. This parameter is responsible for connection at the junction points between different parts of the considered structure. Dependence of solutions on the damage parameter is investigated, in particular, a passage to infinity and to zero is analyzed. Inverse problems are considered provided that the damage parameter and Lamé parameters of the elastic body are unknown. In this case, a displacement of the tip point of the inclusion is assumed to be known. A solution existence of the inverse problems is proved.

KW - Crack

KW - Elastic body

KW - Inverse problem

KW - Non-penetration condition

KW - T-shape inclusion

KW - Variational inequality

UR - http://www.scopus.com/inward/record.url?scp=85102321269&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=46754374

U2 - 10.1016/j.cam.2021.113540

DO - 10.1016/j.cam.2021.113540

M3 - Article

AN - SCOPUS:85102321269

VL - 393

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

M1 - 113540

ER -

ID: 28089162