Abstract

We propose a model for a two-dimensional elastic body with a thin elastic inclusion modeled by a beam equation. Moreover, we assume that a delamination of the inclusion may take place resulting in a crack. Nonlinear boundary conditions are imposed at the crack faces to prevent mutual penetration between the faces. Both variational and differential problem formulations are considered, and existence of solutions is established. Furthermore, we study the dependence of the solution on the rigidity of the embedded beam. It is proved that in the limit cases corresponding to infinite and zero rigidity, we obtain a rigid beam inclusion and cracks with nonpenetration conditions, respectively. Anisotropic behavior of the beam is also analyzed.

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Mathematical Subject Classification 2010

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