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On classical solutions of the Prandtl-Reuss equations of perfect elastoplasticity

Published online by Cambridge University Press:  14 November 2011

Sergej B. Kuksin
Sergej B. Kuksin
Affiliation:
Institut des Hautes Etudes Scientifiques, 35, route de Chartres, 91440-Bures-sur-Y vette, France; Institute for Information Transmission Problems, Ermolovoy St. 19, 101447 Moscow, Russia
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Abstract

We study the elasticity domain for an antiplane deformation of a perfect elastoplastic medium, which is described by the Prandtl-Reuss equations. We prove that a boundary of this domain can be found by solving a system of nonlinear functional equations. In the simplest case of simple shear deformations, this system of equations is studied in detail.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 6 , 1996 , pp. 1297 - 1308
Copyright
Copyright © Royal Society of Edinburgh 1996

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References

1Duvant, G. and Lyons, J. L.. Inequalities in Mechanics and Physics (Berlin: Springer, 1976).CrossRefGoogle Scholar
2Kreiss, H. O.. Initial boundary-value problems for hyperbolic systems. Comm. Pure Appl. Math. 23 (1970), 277–98.CrossRefGoogle Scholar
3Kuksin, S. B.. Generalized solutions of the dynamic problem of perfect elastoplasticity. J. Appl. Math. Mech. 49 (1985), 503–9.CrossRefGoogle Scholar
4Kuksin, S. B.. The boundary of an elasticity domain for the perfect elastoplasticity dynamic problem as a free-boundary problem. In Plasticity and Destruction of Solids (Moscow: Nauka, 1988, in Russian).Google Scholar
5Mandel, J.. Cours de Mecanique des Milieus Continus, Vol. I (Paris: Gauthier-Villars, 1976).Google Scholar
6Volevich, L. R. and Gindikin, S. G.. The method of energy estimates in mixed problems. Russian Math. Surveys 35(5) (1980), 57–137.CrossRefGoogle Scholar