On elastic bodies with thin rigid inclusions and cracks

✍ Scribed by Alexander Khludnev; Günter Leugering

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 238 KB
• Volume: 33
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1308

✦ Synopsis

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.