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Senashov, T. I.; Gomonova, O. V.; Cherepanova, O. N.

Group analysis of the equations of ideal plasticity. (English. Russian original) Zbl 1491.74011

J. Appl. Mech. Tech. Phys. 62, No. 5, 882-889 (2021); translation from Prikl. Mekh. Tekh. Fiz. 62, No. 5, 208-216 (2021).
Summary: This paper deals with the problem of constructing exact solutions of the von Mises three-dimensional equations of plasticity based on the group of continuous transformations admitted by the system (B. D. Annin’s problem). New classes of solutions of the three-dimensional equations of plasticity are given. The problem of compression of an elastoplastic material layer by rigid plates is solved. In this case, the material obeys the exponential plasticity condition proposed by B. D. Annin [“One plane elastoplastic problem with an exponential yield condition” (Russian), Inzh. Zhurn. Mekh. Tverd. Tela 3, 122–123 (1966)].

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
35A30 Geometric theory, characteristics, transformations in context of PDEs

Keywords:

group of continuous transformations; exact solution; conservation law; von Mises three-dimensional ideal plasticity
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References:

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