Geodesic
On rigid inclusions and cavities in elastic body with a crack: non-coercive case
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1024-1041 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper, we consider an equilibrium problem for an elastic body with a crack in a case of Neumann boundary conditions at the external boundary. The Neumann boundary conditions imply a non-coercivity of the problem. Inequality constraints are imposed on the solution providing a mutual non-penetration between the crack faces. Various passages to limit with respect to the parameter characterizing a rigidity of the body are analyzed, and limit models are investigated. In particular, an existence of solutions is proved for all cases considered; necessary and sufficient conditions imposed on the external forces are found. The limit models describe the elastic body with a volume rigid inclusion and the body with a cavity. These results are obtained both for the case when the crack is located inside the elastic body and for the case when it extends to the outer boundary.
Keywords: elastic body, crack, non-coercive boundary value problem, cavity.
Mots-clés : volume rigid inclusion 
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A. M. Khludnev. On rigid inclusions and cavities in elastic body with a crack: non-coercive case. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1024-1041. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a37/

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