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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2015, Volume 19, Number 2, Pages 358–381 (Mi vsgtu1432)  

This article is cited in 1 scientific paper (total in 1 paper)

Mechanics of Solids

Mixed-mode loading of the structural elements with defect

L. V. Stepanova, E. M. Yakovleva

Samara State University, Samara, 443011, Russian Federation

Abstract: In the article the problem of determining the stress-strain state near the mixed-mode crack tip in a power-law material under plane stress conditions is considered. The eigenfunction method is used for the mixed-mode crack tip problem. It is shown that the eigenfunction expansion method results in the nonlinear eigenvalue problem. The numeric solution of the nonlinear eigenvalue problem formulated is obtained. The power of the distance from the crack tip is the eigenvalue of the nonlinear eigenvalue problem considered whereas the angular distributions of the stress components are the eigenfunctions. The new eigenvalues different from the eigenvalues of the Hutchinson–Rice–Rosengren are found. It is shown that the new asymptotic solution can be interpreted as the self-similar intermediate asymptotics of the stress field in the vicinity of the crack tip at distances which are very small compared to the crack length or the size of the specimen and at distances which are large compared to the length of the completely damaged zone. The developed method allows us to construct the geometry of the completely damaged zone in vicinity of the crack tip.

Keywords: nonlinear eigenvalue problem, stress-strain state near the crack tip, mixed-mode loading, mixity parameter, perturbation technique

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-97009-р-Поволжье-а
This work has been supported by the Russian Foundation for Basic Research (project no. 13–01–97009-r-Povolzh'e-a).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1432

Full text: PDF file (3425 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 539.42
MSC: 74R10, 74G70, 74R15, 74A45, 74R20
Original article submitted 13/XII/2014
revision submitted – 11/II/2015

Citation: L. V. Stepanova, E. M. Yakovleva, “Mixed-mode loading of the structural elements with defect”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:2 (2015), 358–381

Citation in format AMSBIB
\Bibitem{SteYak15}
\by L.~V.~Stepanova, E.~M.~Yakovleva
\paper Mixed-mode loading of the structural elements with defect
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 2
\pages 358--381
\mathnet{http://mi.mathnet.ru/vsgtu1432}
\crossref{https://doi.org/10.14498/vsgtu1432}
\zmath{https://zbmath.org/?q=an:06968967}
\elib{http://elibrary.ru/item.asp?id=24078313}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. S. Petukhov, I. E. Keller, “Dvoistvennye zadachi ploskikh polzuschikh techenii stepennoi neszhimaemoi sredy”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:3 (2016), 496–507  mathnet  crossref  zmath  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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