Abstract
In this paper, we consider an overlapping domain problem for two elastic bodies. A glue condition of an equality-type is imposed at a given line. Simultaneously, a part of this line is considered to be a crack face with an inequality-type boundary condition describing mutual non-penetration between crack faces. Variational and differential formulations of the problem are considered. We prove a differentiability of the energy functional in the case of rectilinear cracks and find a formula for invariant integrals. Passage to the limit is justified provided that the rigidity of the body goes to infinity.
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Gaudiello, A., Khludnev, A.M. Crack on the boundary of two overlapping domains. Z. Angew. Math. Phys. 61, 341–356 (2010). https://doi.org/10.1007/s00033-009-0012-4
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DOI: https://doi.org/10.1007/s00033-009-0012-4