Elasticity Problem with a Cusp between Thin Inclusion and Boundary
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 interpenetra...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/12/1081 |
| _version_ | 1797382028600016896 |
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| author | Alexander Khludnev |
| author_facet | Alexander Khludnev |
| author_sort | Alexander Khludnev |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T21:00:28Z |
| format | Article |
| id | doaj.art-4c912dbff8f54acebe24da851b2324ab |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-08T21:00:28Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-4c912dbff8f54acebe24da851b2324ab2023-12-22T13:53:11ZengMDPI AGAxioms2075-16802023-11-011212108110.3390/axioms12121081Elasticity Problem with a Cusp between Thin Inclusion and BoundaryAlexander Khludnev0Lavrentyev Institute of Hydrodynamics of SB RAS, Novosibirsk State University, Novosibirsk 630090, RussiaThis 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.https://www.mdpi.com/2075-1680/12/12/1081elastic bodythin inclusioncuspnon-penetration boundary conditiondamage parameteroptimal control |
| spellingShingle | Alexander Khludnev Elasticity Problem with a Cusp between Thin Inclusion and Boundary Axioms elastic body thin inclusion cusp non-penetration boundary condition damage parameter optimal control |
| title | Elasticity Problem with a Cusp between Thin Inclusion and Boundary |
| title_full | Elasticity Problem with a Cusp between Thin Inclusion and Boundary |
| title_fullStr | Elasticity Problem with a Cusp between Thin Inclusion and Boundary |
| title_full_unstemmed | Elasticity Problem with a Cusp between Thin Inclusion and Boundary |
| title_short | Elasticity Problem with a Cusp between Thin Inclusion and Boundary |
| title_sort | elasticity problem with a cusp between thin inclusion and boundary |
| topic | elastic body thin inclusion cusp non-penetration boundary condition damage parameter optimal control |
| url | https://www.mdpi.com/2075-1680/12/12/1081 |
| work_keys_str_mv | AT alexanderkhludnev elasticityproblemwithacuspbetweenthininclusionandboundary |