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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2010, Volume 51, Issue 1, Pages 117–124 (Mi pmtf1571)  
This article is cited in 3 scientific papers (total in 3 papers)

Self-similar shapes of the free boundary of a nonlinear-viscous band under uniaxial tension

I. E. Keller

Institute of Continuous Media Mechanics, Ural Division, Russian Academy of Sciences, Perm’, 61401, Russia
Full-text PDF (247 kB) Citations (3)
Abstract: An equation of evolution of small perturbations of the free boundary of a nonlinear-viscous band under quasi-static uniaxial tension is derived for studying the necking problem in metals under superplasticity conditions. It is shown that the group of symmetry of this linear parabolic equation is equivalent to the group of symmetry of the linear equation of heat conduction with an arbitrary material parameter of the model. Self-similar solutions are obtained in the form of simple and complicated steady localized structures transferred together with the material of the stretched band.
Keywords: free boundary, solitary waves, nonlinear viscosity, superplasticity, group classification.
Received: 08.12.2008
Accepted: 27.02.2009
English version:
Journal of Applied Mechanics and Technical Physics, 2010, Volume 51, Issue 1, Pages 99–105
DOI: https://doi.org/10.1007/s10808-010-0016-z
Bibliographic databases:
Document Type: Article
UDC: 539.374
Language: Russian
Citation: I. E. Keller, “Self-similar shapes of the free boundary of a nonlinear-viscous band under uniaxial tension”, Prikl. Mekh. Tekh. Fiz., 51:1 (2010), 117–124; J. Appl. Mech. Tech. Phys., 51:1 (2010), 99–105
Citation in format AMSBIB
\Bibitem{Kel10}
\by I.~E.~Keller
\paper Self-similar shapes of the free boundary of a nonlinear-viscous band under uniaxial tension
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2010
\vol 51
\issue 1
\pages 117--124
\mathnet{http://mi.mathnet.ru/pmtf1571}
\elib{https://elibrary.ru/item.asp?id=13026115}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2010
\vol 51
\issue 1
\pages 99--105
\crossref{https://doi.org/10.1007/s10808-010-0016-z}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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