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.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 51, No. 1, pp. 117–124, January–February, 2010.
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Keller, I.É. Self-similar shapes of the free boundary of a nonlinear-viscous band under uniaxial tension. J Appl Mech Tech Phy 51, 99–105 (2010). https://doi.org/10.1007/s10808-010-0016-z
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DOI: https://doi.org/10.1007/s10808-010-0016-z