We consider an equilibrium problem for a 2D elastic body with a thin elastic T-shape inclusion. A part of the inclusion is delaminated from the elastic body forming a crack between the inclusion and the surrounding elastic body. Inequality type boundary conditions are imposed at the crack faces preventing interpenetration between the crack faces. The model is characterized by a damage parameter. This parameter is responsible for connection at the junction points between different parts of the considered structure. Dependence of solutions on the damage parameter is investigated, in particular, a passage to infinity and to zero is analyzed. Inverse problems are considered provided that the damage parameter and Lamé parameters of the elastic body are unknown. In this case, a displacement of the tip point of the inclusion is assumed to be known. A solution existence of the inverse problems is proved.

我们考虑具有薄弹性T形夹杂物的2D弹性体的平衡问题。夹杂物的一部分从弹性体脱层，从而在夹杂物和周围的弹性体之间形成裂纹。在裂纹面上施加不等式边界条件，以防止裂纹之间相互渗透。该模型的特征在于损坏参数。此参数负责在所考虑结构的不同部分之间的连接点处进行连接。研究了解对损伤参数的依赖性，特别是分析了无穷大和零的通过。如果弹性体的损伤参数和Lamé参数未知，则考虑反问题。在这种情况下，假定夹杂物的尖端的位移是已知的。