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On crack problem with overlapping domain
Author(s) -
Khludnev A.M.
Publication year - 2008
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200800019
Subject(s) - rigidity (electromagnetism) , mathematics , domain (mathematical analysis) , nonlinear system , infinity , penetration (warfare) , convergence (economics) , boundary value problem , boundary (topology) , mathematical analysis , structural engineering , physics , engineering , quantum mechanics , operations research , economics , economic growth
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.