On elastic bodies with thin rigid inclusions and cracks |
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Authors: | Alexander Khludnev Günter Leugering |
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Institution: | 1. Lavrentyev Institute of Hydrodynamics of the Russian Academy of Sciences, Novosibirsk 630090, Russia;2. Institute of Applied Mathematics II, Friedrich‐Alexander‐University Erlangen‐Nuremberg, Martensstr. 3, D‐91058 Erlangen, Germany |
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Abstract: | This paper is concerned with the analysis of equilibrium problems for two‐dimensional elastic bodies with thin rigid inclusions and cracks. Inequality‐type boundary conditions are imposed at the crack faces providing a mutual non‐penetration between the crack faces. A rigid inclusion may have a delamination, thus forming a crack with non‐penetration between the opposite faces. We analyze variational and differential problem formulations. Different geometrical situations are considered, in particular, a crack may be parallel to the inclusion as well as the crack may cross the inclusion, and also a deviation of the crack from the rigid inclusion is considered. We obtain a formula for the derivative of the energy functional with respect to the crack length for considering this derivative as a cost functional. An optimal control problem is analyzed to control the crack growth. Copyright © 2010 John Wiley & Sons, Ltd. |
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Keywords: | thin rigid inclusion crack with non‐penetration elastic body delamination of rigid inclusion thick rigid inclusion inequality type boundary conditions |
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