Abstract: 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 su cient 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.

Cite: Khludnev A.M.
On rigid inclusions and cavities in elastic body with a crack: non-coercive case
Сибирские электронные математические известия / Siberian Electronic Mathematical Reports. 2024. V.21. N2. P.1024-1041. DOI: 10.33048/semi.2024.21.068

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