Junction Problem for Elastic Timoshenko Inclusions in Elastic Bodies with a Crack

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