Formation of Cavities and Rigid Inclusions in Composite Materials: Noncoercive Case

We analyze an equilibrium problem for an elastic body with an incorporated thin elastic inclusion delaminated from the surrounding elastic body with inequality type boundary conditions at the crack faces. Neumann type conditions are imposed at the external boundary of the elastic body, which means the noncoercivity of the problem. Assuming that the elasticity tensor depends on a positive parameter, we study the asymptotic behavior of the solutions as the parameter tends to zero and to infinity. The limit models describe an equilibrium state of the elastic body with a rigid inclusion and with a cavity. We establish the existence of a solution in all the cases under consideration.