Junction problem for thin elastic and volume rigid inclusions in elastic body

The article concerns a junction problem for two-dimensional elastic body with a thin elastic inclusion and a volume rigid inclusion. It is assumed that the inclusions have a common point. A delamination of the thin inclusion from the surrounding elastic body is assumed thus forming an interfacial crack. Constraint-type boundary conditions are imposed at the crack faces to prevent interpenetration between the faces. Moreover, a connection between the crack faces is characterized by a positive damage parameter. Limit transitions are justified as the damage parameter tends to infinity and to zero. In addition to this, a transition to limit is analysed as a rigidity parameter of the thin inclusion tends to infinity. Limit models are investigated. In particular, junction conditions at the common point are found for all cases considered. This article is part of the theme issue 'Non-smooth variational problems and applications'.