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IMA Journal of Applied Mathematics Advance Access originally published online on April 27, 2009
IMA Journal of Applied Mathematics 2009 74(3):325-343; doi:10.1093/imamat/hxp017
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A Papkovich–Neuber-based numerical approach to cracks with contact in 3D

M. Hintermüller{dagger}

Department of Mathematics, University of Graz, 8010 Graz, Austria and Chair in Applied Mathematics, University of Sussex, Brighton, BN1 9RF UK

V. A. Kovtunenko

Department of Mathematics, University of Graz, 8010 Graz, Austria and Lavrent'ev Institute of Hydrodynamics, 630090 Novosibirsk, Russia

K. Kunisch

Department of Mathematics, University of Graz, 8010 Graz, Austria

{dagger} Email: michael.hintermueller{at}uni-graz.at

Received on January 30, 2007; Accepted on February 24, 2009

The mathematical model of a crack with non-penetration conditions is considered in the framework of 3D elasticity. The spatial crack problem is investigated with respect to its numerical realization in the context of constrained optimization. Specifically, for homogeneous isotropic solids with planar cracks, a Papkovich–Neuber-based representation is adopted. It allows to employ a primal–dual active set strategy with an unconditional global and monotone convergence property. The iterates turn out to be primally feasible. Illustrative numerical examples are presented.

Keywords: crack with non-penetration; constrained optimization problem; primal–dual active set algorithm; Papkovich–Neuber representation; numerical calculation.


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