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On modeling thin inclusions in elastic bodies with a damage parameter. / Khludnev, A. M.

In: Mathematics and Mechanics of Solids, Vol. 24, No. 9, 01.09.2019, p. 2742-2753.

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

Harvard

Khludnev, AM 2019, 'On modeling thin inclusions in elastic bodies with a damage parameter', Mathematics and Mechanics of Solids, vol. 24, no. 9, pp. 2742-2753. https://doi.org/10.1177/1081286518796472

APA

Khludnev, A. M. (2019). On modeling thin inclusions in elastic bodies with a damage parameter. Mathematics and Mechanics of Solids, 24(9), 2742-2753. https://doi.org/10.1177/1081286518796472

Vancouver

Khludnev AM. On modeling thin inclusions in elastic bodies with a damage parameter. Mathematics and Mechanics of Solids. 2019 Sept 1;24(9):2742-2753. doi: 10.1177/1081286518796472

Author

Khludnev, A. M. / On modeling thin inclusions in elastic bodies with a damage parameter. In: Mathematics and Mechanics of Solids. 2019 ; Vol. 24, No. 9. pp. 2742-2753.

BibTeX

@article{243e5ca4de8b4a5386487567aa83ca8a,
title = "On modeling thin inclusions in elastic bodies with a damage parameter",
abstract = "In this paper, we analyze equilibrium problems for 2D elastic bodies with two thin inclusions in the presence of damage. A delamination of the inclusions from the matrix is assumed, thus forming a crack between the elastic body and the inclusions. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are discussed. The paper provides an asymptotic analysis with respect to the damage parameter. An optimal control problem is analyzed with a cost functional to be equal to the derivative of the energy functional with respect to the crack length, and the damage parameter being a control function.",
keywords = "crack, damage parameter, delamination, derivative of energy functional, non-penetration boundary condition, optimal control problem, Thin inclusion, variational inequality",
author = "Khludnev, {A. M.}",
year = "2019",
month = sep,
day = "1",
doi = "10.1177/1081286518796472",
language = "English",
volume = "24",
pages = "2742--2753",
journal = "Mathematics and Mechanics of Solids",
issn = "1081-2865",
publisher = "SAGE Publications Inc.",
number = "9",

}

RIS

TY - JOUR

T1 - On modeling thin inclusions in elastic bodies with a damage parameter

AU - Khludnev, A. M.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - In this paper, we analyze equilibrium problems for 2D elastic bodies with two thin inclusions in the presence of damage. A delamination of the inclusions from the matrix is assumed, thus forming a crack between the elastic body and the inclusions. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are discussed. The paper provides an asymptotic analysis with respect to the damage parameter. An optimal control problem is analyzed with a cost functional to be equal to the derivative of the energy functional with respect to the crack length, and the damage parameter being a control function.

AB - In this paper, we analyze equilibrium problems for 2D elastic bodies with two thin inclusions in the presence of damage. A delamination of the inclusions from the matrix is assumed, thus forming a crack between the elastic body and the inclusions. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. Weak and strong formulations of the problems are discussed. The paper provides an asymptotic analysis with respect to the damage parameter. An optimal control problem is analyzed with a cost functional to be equal to the derivative of the energy functional with respect to the crack length, and the damage parameter being a control function.

KW - crack

KW - damage parameter

KW - delamination

KW - derivative of energy functional

KW - non-penetration boundary condition

KW - optimal control problem

KW - Thin inclusion

KW - variational inequality

UR - http://www.scopus.com/inward/record.url?scp=85052604012&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=35739316

U2 - 10.1177/1081286518796472

DO - 10.1177/1081286518796472

M3 - Article

AN - SCOPUS:85052604012

VL - 24

SP - 2742

EP - 2753

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

SN - 1081-2865

IS - 9

ER -

ID: 23583944