On elastic bodies with thin rigid inclusions and cracks
Khludnev AM, Leugering G (2010)
Publication Type: Journal article
Publication year: 2010
Journal
Publisher: Wiley-Blackwell
Book Volume: 33
Pages Range: 1955--1967
Volume: 33
DOI: 10.1002/mma.1308
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.
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Russian Federation (RU)How to cite
APA:
Khludnev, A.M., & Leugering, G. (2010). On elastic bodies with thin rigid inclusions and cracks. Mathematical Methods in the Applied Sciences, 33, 1955--1967. https://doi.org/10.1002/mma.1308
MLA:
Khludnev, A. M., and Günter Leugering. "On elastic bodies with thin rigid inclusions and cracks." Mathematical Methods in the Applied Sciences 33 (2010): 1955--1967.
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