Slow deformation fronts: model and features of distribution
https://doi.org/10.5800/GT-2018-9-3-0370
Abstract
Our study aimed at investigating the origin and development of ‘slow’ movements in a solid body/medium under loading and studying the role of such movements in the occurrence of critical states, i.e. sources of destruction in a stable solid medium. Computerized modeling was conducted to simulate the evolution of the stress-strain state and the formation of slow deformation waves in a loaded medium. We have developed and justified a mathematical model of the loaded elastoplastic medium, which demonstrates the joint generation and propagation of ordinary stress waves (propagating with the velocity of sound) and slow deformation waves of the inelastic nature. The propagation rates of the latter are 5–7 orders of magnitude lower than the velocity of sound. The features of slow deformation wave propagation in the solid media are investigated. In the model, slow deformation waves interact under certain conditions as solitons and penetrate each other. Considering the properties, they are similar to both solitons satisfying the solutions of the non-linear Korteweg – de Vries equation and kinks satisfying the solutions of the sin-Gordon equation. Slow deformation fronts are actively involved into the formation of sources of destruction and provide an effective mechanism for the transfer and redistribution of energy in the loaded medium.
About the Authors
P. V. Makarov
Institute of Strength Physics and Materials Science, Siberian Branch of RAS;
Tomsk State University
Russian Federation
Russian Federation
Pavel V. Makarov, Doctor of Physics and Mathematics, Head of Laboratory,
Institute of Strength Physics and Materials Science, Siberian Branch of RAS
2/4 Akademicheskii ave., Tomsk 634055; 50 Lenin ave., Tomsk 634050
Yu. A. Khon
Institute of Strength Physics and Materials Science, Siberian Branch of RAS
Russian Federation
Russian Federation
Yuri A. Khon, Doctor of Physics and Mathematics, Head of Laboratory
2/4 Akademicheskii ave., Tomsk 634055
A. Yu. Peryshkin
Institute of Strength Physics and Materials Science, Siberian Branch of RAS
Russian Federation
Russian Federation
Aleksei Yu. Peryshkin, Engineer
2/4 Akademicheskii ave., Tomsk 634055
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Review
For citations:
Makarov P.V., Khon Yu.A., Peryshkin A.Yu. Slow deformation fronts: model and features of distribution. Geodynamics & Tectonophysics. 2018;9(3):755-769. (In Russ.) https://doi.org/10.5800/GT-2018-9-3-0370
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