gtcrustГеодинамика и тектонофизикаGeodynamics & Tectonophysics2078-502XInstitute of the Earth's crust of the Russian Academy of Sciences, Siberian Branch10.5800/GT-2018-9-3-0370gtcrust-624Research ArticleТЕКТОНОФИЗИКАTECTONOPHYSICSМЕДЛЕННЫЕ ДЕФОРМАЦИОННЫЕ ФРОНТЫ. МОДЕЛЬ И ОСОБЕННОСТИ РАСПРОСТРАНЕНИЯSLOW DEFORMATION FRONTS: MODEL AND FEATURES OF DISTRIBUTIONhttps://orcid.org/0000-0003-0541-5128МакаровП. В.MakarovP. V.

Павел Васильевич Макаров, докт. физ.-мат. наук, зав. лабораториейИнститута физики прочности и материаловедения СО РАН 

634055, Томск, проспект Академический, 2/4; 634050, Томск, просп. Ленина, 50

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

pvm@ispms.ruХонЮ. А.KhonYu. A.

Юрий Андреевич Хон, докт. физ.-мат. наук, зав. лабораторией 

634055, Томск, проспект Академический, 2/4

Yuri A. Khon, Doctor of Physics and Mathematics, Head of Laboratory 

2/4 Akademicheskii ave., Tomsk 634055

Khon@ispms.ruПерышкинА. Ю.PeryshkinA. Yu.

Алексей Юрьевич Перышкин, инженер 

634055, Томск, проспект Академический, 2/4

Aleksei Yu. Peryshkin, Engineer

2/4 Akademicheskii ave., Tomsk 634055

alexb700@yandex.ruИнститут физики прочности и материаловедения СО РАН; Томский государственный университетРоссияInstitute of Strength Physics and Materials Science, Siberian Branch of RAS; Tomsk State UniversityRussian FederationИнститут физики прочности и материаловедения СО РАНРоссияInstitute of Strength Physics and Materials Science, Siberian Branch of RASRussian Federation20180810201893755769Copyright © Макаров П.В., Хон Ю.А., Перышкин А.Ю., 20182018Макаров П.В., Хон Ю.А., Перышкин А.Ю.Makarov P.V., Khon Y.A., Peryshkin A.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.gt-crust.ru/jour/article/view/624

Цель работы заключалась в разработке модельных представлений о природе «медленных» движений в нагружаемых твердых телах и средах и в изучении их роли в формировании критических состояний – очагов разрушения в прочной среде. Методика исследований – численное моделирование эволюции напряженно-деформированного состояния и формирования в нагружаемой среде медленных волн деформации. Разработан и обоснован вариант математической модели описания процессов совместной генерации и распространения в нагружаемых упругопластических средах как обычных волн напряжений, распространяющихся со скоростями звука, так и медленных деформационных волн неупругой природы, скорости которых на 5–7 порядков ниже скоростей звука. Исследованы особенности распространения медленных деформационных волн в прочных средах. Показано, что медленные деформационные волны при определенных условиях взаимодействуют как солитоны, проникая друг через друга. Их свойства сходны со свойствами как солитонов, получаемых решениями нелинейного уравнения Кортевега – де-Фриза, так и кинков – решений уравнения sin-Гордона. Показано, что медленные деформационные фронты активно участвуют в формировании очага разрушения, являясь эффективным механизмом переноса и перераспределения энергии в нагружаемой среде.

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.

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The authors declare that there are no conflicts of interest present.