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Some Modern Methods in Mechanics of Cracks

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Modern Analysis and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 191))

Abstract

An application of some modern methods to studying cracks in aligned composites and an interaction of curvilinear cracks with an interface is presented. The first method based on Novozhilov’s hybrid model is focused on estimation of variation intervals of sizes of a partially bridged equilibrium crack and bridging zone. The problem of a slightly curved crack near an interface is solved by a combination of some methods which are Muskhelishvili’s method of complex potentials, an original superposition method reduced to Fredholm integral equations of the second type, and the boundary perturbation method.

This work was supported by Russian Foundation for Basic Research under grants 05-01-00274 and 06-01-00452.

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Author information

Authors and Affiliations

  1. Faculty of Applied Mathematics, St. Petersburg State University, Universitetski pr., 35, St. Petersburg, 198504, Russia

    Mikhail A. Grekov

  2. Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetski pr., 28, St. Petersburg, 198504, Russia

    Nikita F. Morozov

Authors
  1. Mikhail A. Grekov
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  2. Nikita F. Morozov
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Vadim M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    Israel Gohberg

  3. Insitute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivska st., 01601, Kyiv-4, Ukraine

    Anatoly Kochubei , Yurij Berezansky , Myroslav Gorbachuk  & Valentyna Gorbachuk , ,  & 

  4. Department of Mathematical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Gennadiy Popov

  5. Institute of Analysis and Scientific Computing, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Heinz Langer

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Grekov, M.A., Morozov, N.F. (2009). Some Modern Methods in Mechanics of Cracks. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 191. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9921-4_8

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