Junction Problem for Elastic Timoshenko Inclusionsin Elastic Bodies with a Crack

The paper is concerned with a junction problem for Timoshenko elastic inclusions placed in an elastic body with a crack. It is assumed that the crack crosses the thin inclusion at some point. This point is a mutual contact point. Inequality-type boundary conditions are imposed at the point of contact and on the crack edges to prevent mutual penetration between inclusion parts and crack edges, respectively. Existence and uniqueness theorems are established. Differential formulation in the form of a boundary value problem that contains junction boundary conditions is presented.