Elasticity problem with a cusp between thin inclusion and boundary Full article
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Axioms
ISSN: 2075-1680 |
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| Output data | Year: 2023, Volume: 12, Number: 12, Article number : 1081, Pages count : 15 DOI: 10.3390/axioms12121081 | ||||
| Tags | elastic body; thin inclusion; cusp; non-penetration boundary condition; damage parameter; optimal control | ||||
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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
Cite:
Khludnev A.
Elasticity problem with a cusp between thin inclusion and boundary
Axioms. 2023. V.12. N12. 1081 :1-15. DOI: 10.3390/axioms12121081 WOS РИНЦ OpenAlex
Elasticity problem with a cusp between thin inclusion and boundary
Axioms. 2023. V.12. N12. 1081 :1-15. DOI: 10.3390/axioms12121081 WOS РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:001131101200001 |
| Elibrary: | 54911159 |
| OpenAlex: | W4389056227 |