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IssuesArchive of Issues2008-5pp.756-764

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Yu. N. Radaev, "On the hyperbolicity of 3D plasticity equations in isostatic coordinates," Mech. Solids. 43 (5), 756-764 (2008)
Year 2008 Volume 43 Number 5 Pages 756-764
DOI 10.3103/S0025654408050105
Title On the hyperbolicity of 3D plasticity equations in isostatic coordinates
Author(s) Yu. N. Radaev (Samara State University, Akad. Pavlova 1, Samara, 443011, Russia, radayev@ssu.samara.ru)
Abstract We consider the problem of classifying partial differential equations of the three-dimensional problem of ideal plasticity (for stress states corresponding to an edge of the Tresca prism) and the problem of finding a change of independent variables reducing these equations to the simplest normal Cauchy form. The original system of equations is represented in an isostatic coordinate system and is substantially nonlinear. We state a criterion for the simplest normal Cauchy form and find a coordinate system reducing the original system to the simplest normal Cauchy form. We show that the condition obtained in the present paper for a system to take the simplest normal form is stronger than the Petrovskii t-hyperbolicity condition if t is understood as the canonical isostatic coordinate whose level surfaces in space form fibers normal to the principal direction field corresponding to the maximum (minimum) principal stress.
Received 02 December 2005
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