Abstract:
We study simple one-dimensional waves (Riemann waves) in an incompressible anisotropic elastoplastic medium with hardening. The motion is parallel to the planes of constant phase. We show that there exist two types of such waves: fast and slow waves, whose velocities are different everywhere except for some points in the plane of stress components. The medium is assumed to be nonlinear and defined by its elastic properties as well as by conditions for the formation of plastic deformations. We find the velocities of the characteristics that carry the Riemann waves, and analyze the evolution of the Riemann waves and the overturning conditions for these waves.
Citation:
A. G. Kulikovskii, A. P. Chugainova, “Simple One-Dimensional Waves in an Incompressible Anisotropic Elastoplastic Medium with Hardening”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 189–198; Proc. Steklov Inst. Math., 310 (2020), 175–184
\Bibitem{KulChu20}
\by A.~G.~Kulikovskii, A.~P.~Chugainova
\paper Simple One-Dimensional Waves in an Incompressible Anisotropic Elastoplastic Medium with Hardening
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 310
\pages 189--198
\publ Steklov Math. Inst.
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm4108}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2020
\vol 310
\pages 175--184
\crossref{https://doi.org/10.1134/S0081543820050144}
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Linking options:
https://www.mathnet.ru/eng/tm4108
https://doi.org/10.4213/tm4108
https://www.mathnet.ru/eng/tm/v310/p189
This publication is cited in the following 1 articles:
A. P. Chugainova, A. G. Kulikovskii, “Shock waves in an incompressible anisotropic elastoplastic medium with hardening and their structures”, Appl. Math. Comput., 401 (2021), 126077
Citation in format AMSBIB
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