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The paper is concerned with an equilibrium problem for 2D elastic body with a thin elastic Timoshenko inclusion and a thin rigid inclusion. The elastic inclusion is assumed to be delaminated from the elastic body thus forming an interfacial crack with the matrix. Inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration. A connection between two inclusions at a given point is characterized by a positive damage parameter. Existence of solutions of the problem considered is proved, and different equivalent formulations of the problem are analyzed; junction conditions at the connection point are found. A convergence of solutions as the damage parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is analyzed. An analysis of the limit models is performed. A solution existence of an inverse problem for finding the damage and rigidity parameters is proved provided that an additional information concerning the derivative of the energy functional with respect to the delamination length is given. [ABSTRACT FROM AUTHOR]

The paper concerns an analysis of equilibrium problems for 2D elastic bodies with a thin Timoshenko inclusion crossing an external boundary at zero angle. The inclusion is assumed to be delaminated, thus forming a crack between the inclusion and the body. We consider elastic inclusions as well as rigid inclusions. To prevent a mutual penetration between the crack faces, inequality type boundary conditions are imposed at the crack faces. Theorems of existence and uniqueness are established. Passages to limits are investigated as a rigidity parameter of the elastic inclusion going to infinity. [ABSTRACT FROM AUTHOR]

We consider an equilibrium problem for 2D elastic body with a thin inclusion crossing an external boundary at zero angle. It is assumed that the inclusion is delaminated, therefore a crack between the inclusion and the body is considered. To prevent a mutual penetration between crack faces, inequality type boundary conditions are imposed at the crack faces. We analyze elastic inclusions as well as rigid inclusions. Passages to limits are investigated as a rigidity parameter of the inclusion goes to infinity. Theorems of existence and uniqueness are proved. [ABSTRACT FROM AUTHOR]

We consider an asymptotic behaviour of a solution near a tip of a rigid line inclusion in two dimensional homogeneous isotropic linearized elasticity. By means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution around there. Furthermore, we give expressions of the invariant integral and the Irwin's formula. [ABSTRACT FROM AUTHOR]

Abstract: A topological derivative is defined, which is caused by kinking of a crack, thus, representing the topological change. Using variational methods, the anti-plane model of a solid subject to a non-penetration condition imposed at the kinked crack is considered. The objective function of the potential energy is expanded with respect to the diminishing branch of the incipient crack. The respective sensitivity analysis is provided by a Saint-Venant principle and a local decomposition of the solution of the variational problem in the Fourier series. [ABSTRACT FROM AUTHOR]

Overlapping domain problem describing an equilibrium state for two elastic bodies with a crack is analyzed. Nonlinear boundary conditions are considered providing a mutual non-penetration between the crack faces. We prove a solution existence for the problem with suitable boundary conditions imposed at a glue set. The main interest of the paper is the derivative of the energy functional with respect to the crack length. Assuming the rigidity of the second body is increasing to infinity a convergence in the formula for the derivative of energy functionals is established. [ABSTRACT FROM AUTHOR]