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On crack propagations in elastic bodies with thin inclusions. / Khludnev, A. M.; Popova, T. S.

In: Сибирские электронные математические известия, Vol. 14, 01.01.2017, p. 586-599.

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

Harvard

Khludnev, AM & Popova, TS 2017, 'On crack propagations in elastic bodies with thin inclusions', Сибирские электронные математические известия, vol. 14, pp. 586-599. https://doi.org/10.17377/semi.2017.14.050

APA

Khludnev, A. M., & Popova, T. S. (2017). On crack propagations in elastic bodies with thin inclusions. Сибирские электронные математические известия, 14, 586-599. https://doi.org/10.17377/semi.2017.14.050

Vancouver

Khludnev AM, Popova TS. On crack propagations in elastic bodies with thin inclusions. Сибирские электронные математические известия. 2017 Jan 1;14:586-599. doi: 10.17377/semi.2017.14.050

Author

Khludnev, A. M. ; Popova, T. S. / On crack propagations in elastic bodies with thin inclusions. In: Сибирские электронные математические известия. 2017 ; Vol. 14. pp. 586-599.

BibTeX

@article{df62b0730312406db190a3c828f2cb63,
title = "On crack propagations in elastic bodies with thin inclusions",
abstract = "The paper concerns an analysis of a crack propagation phenomena for an elastic body with thin inclusions and cracks. In the frame of free boundary approach, we investigate a dependence of the solutions on a rigidity parameter of the inclusion. A passage to the limit is justified as the parameter goes to infinity. Derivatives of the energy functionals are found with respect to the crack length for the models considered with different rigidity parameters. The Griffith criterion is used to describe a crack propagation. In so doing, an optimal control problem is investigated with a rigidity parameter being a control function. A cost functional coincides with a derivative of the energy functional with respect to the crack length. A solution existence is proved.",
keywords = "Crack, Delamination, Nonpenetration boundary condition, Optimal control, Semirigid inclusion, Thin elastic inclusion, Timoshenko beam",
author = "Khludnev, {A. M.} and Popova, {T. S.}",
year = "2017",
month = jan,
day = "1",
doi = "10.17377/semi.2017.14.050",
language = "English",
volume = "14",
pages = "586--599",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - On crack propagations in elastic bodies with thin inclusions

AU - Khludnev, A. M.

AU - Popova, T. S.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The paper concerns an analysis of a crack propagation phenomena for an elastic body with thin inclusions and cracks. In the frame of free boundary approach, we investigate a dependence of the solutions on a rigidity parameter of the inclusion. A passage to the limit is justified as the parameter goes to infinity. Derivatives of the energy functionals are found with respect to the crack length for the models considered with different rigidity parameters. The Griffith criterion is used to describe a crack propagation. In so doing, an optimal control problem is investigated with a rigidity parameter being a control function. A cost functional coincides with a derivative of the energy functional with respect to the crack length. A solution existence is proved.

AB - The paper concerns an analysis of a crack propagation phenomena for an elastic body with thin inclusions and cracks. In the frame of free boundary approach, we investigate a dependence of the solutions on a rigidity parameter of the inclusion. A passage to the limit is justified as the parameter goes to infinity. Derivatives of the energy functionals are found with respect to the crack length for the models considered with different rigidity parameters. The Griffith criterion is used to describe a crack propagation. In so doing, an optimal control problem is investigated with a rigidity parameter being a control function. A cost functional coincides with a derivative of the energy functional with respect to the crack length. A solution existence is proved.

KW - Crack

KW - Delamination

KW - Nonpenetration boundary condition

KW - Optimal control

KW - Semirigid inclusion

KW - Thin elastic inclusion

KW - Timoshenko beam

UR - http://www.scopus.com/inward/record.url?scp=85042740604&partnerID=8YFLogxK

U2 - 10.17377/semi.2017.14.050

DO - 10.17377/semi.2017.14.050

M3 - Article

AN - SCOPUS:85042740604

VL - 14

SP - 586

EP - 599

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 10220974