On the mechanical interplay between Timoshenko and semirigid inclusions embedded in elastic bodies

In the paper, an equilibrium problem for elastic bodies with a thin elastic Timoshenko inclusion and a thin semirigid inclusion is analyzed. The inclusions are assumed to be delaminated from elastic bodies, thus forming a crack between the inclusions and the elastic matrix. Nonlinear boundary conditions are imposed at the crack faces to prevent a mutual penetration between the crack faces. The inclusions have a joint point. A passage to a limit is investigated as a rigidity parameter of the elastic inclusion goes to infinity. The limit model is investigated. Junction boundary conditions are found at the joint point for the problem analyzed as well as for the limit problem.