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Constrained optimization for interface cracks in composite materials subject to non-penetration conditions

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Abstract

A constrained problem for a composite material with an interface crack subject to non-penetration conditions is considered. The response of a composite consisting of two identical homogeneous orthotropic materials is described with respect to in-plane deformation. The coupling of the materials occurs at an interface with angle between their vertical planes of elastic symmetry. The model is not split into independent in-plane and anti-plane states. Well-posedness of the problem is proved by variational methods. For numerical computations, a semi-smooth Newton method is proposed and its convergence is studied. Using the proposed algorithms, numerical experiments for an interface crack under mode-3 loading are presented and analyzed with respect to the half-angle defining the coupling.

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Authors and Affiliations

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

    M. Hintermüller, V. A. Kovtunenko & K. Kunisch

  2. Lavrent’ev Institute of Hydrodynamics, 630090, Novosibirsk, Russia

    V. A. Kovtunenko

Authors
  1. M. Hintermüller
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  2. V. A. Kovtunenko
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  3. K. Kunisch
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Correspondence to M. Hintermüller.

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Hintermüller, M., Kovtunenko, V.A. & Kunisch, K. Constrained optimization for interface cracks in composite materials subject to non-penetration conditions. J Eng Math 59, 301–321 (2007). https://doi.org/10.1007/s10665-006-9113-7

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  • DOI: https://doi.org/10.1007/s10665-006-9113-7

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