We analyze an equilibrium problem for 2D elastic body with a T-shape thin inclusion in presence of damage. A part of the inclusion is elastic, and the other part is a rigid one. A delamination of the inclusion from the elastic body is assumed, thus forming a crack between the elastic body and the inclusion. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces. The damage is characterized by a positive parameter. The paper provides an asymptotic analysis of the solutions as the damage parameter tends to infinity and to zero. A passage to infinity of a rigidity parameter of the elastic part of the inclusion is also analyzed. Junction conditions are determined at the connection point between the elastic and rigid parts of the inclusion. An existence theorem is proved for an inverse problem of finding displacement fields and the damage and rigidity parameters provided that a displacement of the tip point of the inclusion is known.

我们分析了存在损伤时T形薄夹杂物的2D弹性体的平衡问题。夹杂物的一部分是弹性的，另一部分是刚性的。假定夹杂物从弹性体剥离，从而在弹性体和夹杂物之间形成裂纹。裂纹面的非线性边界条件被认为可以防止裂纹面之间的相互渗透。损坏的特征在于正参数。由于损伤参数趋于无穷大和趋于零，因此本文提供了渐近分析的解。还分析了夹杂物的弹性部分的刚度参数的无穷大。在夹杂物的弹性和刚性部分之间的连接点确定接合条件。