One-Dimensional Interaction of a Cylindrical Unloading wave with a Moving Elastic Plastic Boundary
E. A. Gerasimenko1, L. V. Kovtanyuk1, A. A. Burenin2,3
1Institute of Automation and Control Processes, Far East Branch of the Russian Academy of Sciences, Vladivostok, 69004, Russia
2Institute of Engineering Science and Metallurgy, Far East Branch of the Russian Academy of Sciences, Komsomolsk-on-Amur, 681005, Russia
3Komsomolsk-on-Amur State Technical University, Komsomolsk-on-Amur, 681013, Russia
Keywords: большие деформации, упругость, вязкость, пластичность, ударная волна, волна разгрузки, large deformations, elasticity, viscosity, plasticity, shock wave, unloading wave
Abstract
The one-dimensional dynamic problem of the interaction of the unloading wave with the elastic-plastic boundary is considered within the theory of large elastic-plastic deformations. It is shown that before the formation of the unloading wave, the increasing pressure gradient leads to quasistatic deformation of the elastic-viscoplastic material filling the round tube, which is retained in the tube due to friction about its wall, resulting in the formation of near-wall viscoplastic flow and an elastic core. The unloading wave is initiated at the moment when the material begins to slip on the inner wall of the tube. Calculations were conducted using the ray method of constructing approximate solutions behind strong discontinuity surfaces, and ray expansions of the solutions behind the cylindrical surfaces of discontinuities were obtained.
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