This article is cited in 1 paper

Differentical equations, dynamical systems and optimal control

On rigid inclusions and cavities in elastic body with a crack: non-coercive case

A. M. Khludnev

Lavrentyev Institute of Hydrodynamics of SB RAS, pr. Lavrentieva, 15, 630090, Novosibirsk, Russia

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 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, volume rigid inclusion, cavity.

UDC: 517.95, 539.3

MSC: 35J88, 35Q74

Received April 5, 2024, published November 8, 2024

Language: English

DOI: 10.33048/semi.2024.21.068