Mathematical Modeling of a T-Shaped Junction of Thin Anisotropic Inclusions in an Elastic Body in the Presence of Delamination

The deformation of an elastic body containing two thin anisotropic inclusions intersecting at a right angle is studied using a mathematical model with unilateral boundary conditions. The inclusions intersect at an interior point of one of them to form a T-shaped structure in the elastic body. One of the inclusions delaminates from the matrix to form a crack. Inequality type boundary conditions are specified on the faces of the cut. Numerical solution of the problem in the domain with the cut is performed by a domain decomposition method using a Uzawa type algorithm. A method based on space decomposition into a direct sum of subspaces is used to determine the displacement functions of the semirigid inclusion.