On Orthogonal Junction of Thin Semi-Rigid Inclusions in a Two-Dimensional Elastic Body
摘要
In this paper, we study the problem of equilibrium of a two-dimensional elastic body containing two thin anisotropic inclusions. The inclusions model is characterized by a given structure of displacement functions and rotation angles. The inclusions intersect, forming a T-shaped system in an elastic matrix. Two cases of junction are considered: in the absence of a connection between the inclusions and for the case of perfect adhesion between them. It is assumed that one of the inclusions delaminates from the elastic matrix forming a crack. Due to the presence of a crack, the elastic body occupies a domain with a cut, while on the cut edges, as on a part of the boundary, boundary conditions of the form of inequalities are set. The problem is posed as a variational one, and a complete differential formulation in the form of a boundary value problem is also obtained, including the junction conditions at a joint point of inclusions. The equivalence of the variational and differential formulations of the problem is proved under the condition of sufficient smoothness of the solutions