Optimal control of cracks in elastic bodies with thin rigid inclusions

Khludnev AM, Leugering G (2011)

Publication Type: Journal article

Publication year: 2011

Journal

ZAMM - Zeitschrift für angewandte Mathematik und Mechanik Wiley-VCH Verlag

Publisher: Wiley-VCH Verlag

Book Volume: 91

Pages Range: 125--137

Volume: 91

Issue: 2

Journal Issue: 2

DOI: 10.1002/zamm.201000058

Abstract

In this paper we consider the control of cracks in elastic bodies with rigid inclusion. We first describe the problem statement, provide an equivalent formulation as a variational inequality and prove existence and uniqueness of solutions. Furthermore, we consider this problem as a limiting problem when the elasticity parameters of the inclusion tend to infinity. Then we formulate the optimal control problems and derive an explicit formula for the crack sensitivity and for the energy release rate. We show existence of optimal solutions.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik

Additional Organisation(s)

Exzellenz-Cluster Engineering of Advanced Materials

Involved external institutions

Russian Academy of Sciences / Росси́йская акаде́мия нау́к (RAS) RU Russian Federation (RU)

How to cite

APA:

Khludnev, A.M., & Leugering, G. (2011). Optimal control of cracks in elastic bodies with thin rigid inclusions. ZAMM - Zeitschrift für angewandte Mathematik und Mechanik, 91(2), 125--137. https://dx.doi.org/10.1002/zamm.201000058

MLA:

Khludnev, Alexander M., and Günter Leugering. "Optimal control of cracks in elastic bodies with thin rigid inclusions." ZAMM - Zeitschrift für angewandte Mathematik und Mechanik 91.2 (2011): 125--137.

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