Elasticity Problem with a Cusp between Thin Inclusion and Boundary

Standard

Elasticity Problem with a Cusp between Thin Inclusion and Boundary. / Khludnev, Alexander.

In: Axioms, Vol. 12, No. 12, 27.11.2023, p. 1081.

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

BibTeX

@article{d57153b6ed32410fbaee57b0c9622632,

title = "Elasticity Problem with a Cusp between Thin Inclusion and Boundary",

abstract = "This paper concerns an equilibrium problem for an an elastic body with a thin rigid inclusion crossing an external boundary of the body at zero angle. The inclusion is assumed to be exfoliated from the surrounding elastic material that provides an interfacial crack. To avoid nonphysical interpenetration of the opposite crack faces, we impose inequality type constraints. Moreover, boundary conditions at the crack faces depend on a positive parameter describing a cohesion. A solution existence of the problem with different conditions on the external boundary is proved. Passages to the limit are analyzed as the damage parameter tends to infinity and to zero. Finally, an optimal control problem with a suitable cost functional is investigated. In this case, a part of the rigid inclusion is located outside of the elastic body, and a control function is a shape of the inclusion.",

keywords = "ELASTIC BODY, Thin inclusion, CUSP, Non-penetration boundary conditions, Damage parameter, Optimal control",

author = "Alexander Khludnev",

note = "This work is supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation. Khludnev, A. M. Elasticity problem with a cusp between thin inclusion and boundary / A. M. Khludnev // Axioms. – 2023. – Vol. 12, No. 12. – P. 1081. – DOI 10.3390/axioms12121081.",

year = "2023",

month = nov,

day = "27",

doi = "10.3390/axioms12121081",

language = "English",

volume = "12",

pages = "1081",

journal = "Axioms",

issn = "2075-1680",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "12",

}

RIS

TY - JOUR

T1 - Elasticity Problem with a Cusp between Thin Inclusion and Boundary

AU - Khludnev, Alexander

N1 - This work is supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2022-282 with the Ministry of Science and Higher Education of the Russian Federation. Khludnev, A. M. Elasticity problem with a cusp between thin inclusion and boundary / A. M. Khludnev // Axioms. – 2023. – Vol. 12, No. 12. – P. 1081. – DOI 10.3390/axioms12121081.

PY - 2023/11/27

Y1 - 2023/11/27

N2 - This paper concerns an equilibrium problem for an an elastic body with a thin rigid inclusion crossing an external boundary of the body at zero angle. The inclusion is assumed to be exfoliated from the surrounding elastic material that provides an interfacial crack. To avoid nonphysical interpenetration of the opposite crack faces, we impose inequality type constraints. Moreover, boundary conditions at the crack faces depend on a positive parameter describing a cohesion. A solution existence of the problem with different conditions on the external boundary is proved. Passages to the limit are analyzed as the damage parameter tends to infinity and to zero. Finally, an optimal control problem with a suitable cost functional is investigated. In this case, a part of the rigid inclusion is located outside of the elastic body, and a control function is a shape of the inclusion.

AB - This paper concerns an equilibrium problem for an an elastic body with a thin rigid inclusion crossing an external boundary of the body at zero angle. The inclusion is assumed to be exfoliated from the surrounding elastic material that provides an interfacial crack. To avoid nonphysical interpenetration of the opposite crack faces, we impose inequality type constraints. Moreover, boundary conditions at the crack faces depend on a positive parameter describing a cohesion. A solution existence of the problem with different conditions on the external boundary is proved. Passages to the limit are analyzed as the damage parameter tends to infinity and to zero. Finally, an optimal control problem with a suitable cost functional is investigated. In this case, a part of the rigid inclusion is located outside of the elastic body, and a control function is a shape of the inclusion.

KW - ELASTIC BODY

KW - Thin inclusion

KW - CUSP

KW - Non-penetration boundary conditions

KW - Damage parameter

KW - Optimal control

UR - https://www.mendeley.com/catalogue/51abdbd7-9ae7-3ab8-8eec-fcf4fe33f6d1/

UR - https://elibrary.ru/item.asp?id=54911159

U2 - 10.3390/axioms12121081

DO - 10.3390/axioms12121081

M3 - Article

VL - 12

SP - 1081

JO - Axioms

JF - Axioms

SN - 2075-1680

IS - 12

ER -

ID: 71527977