Медленные деформационные фронты. Модель и особенности распространения

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.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

Slow deformation fronts: model and features of distribution

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

Autosoliton view of the seismic process. Part 1. possibility of generation and propagation of slow deformation autosoliton disturbances in geomedia

A new autosoliton view is developed for the seismic process. In physical terms, faults correspond to stationary autosolitons, and inter- and intrafault deformation disturbances are traveling autosolitons. Slow dynamics reveals itself only on large time scales because slow autosoliton disturbances, as a rule, have velocities 4–7 orders of magnitude lower than the sound velocity. It is shown that, in the loaded strong medium, slow autowave and autosoliton disturbances are generated by short dynamic actions (pulses) at interfaces. In real geomaterials, these are block boundaries and various-scale faults. Dynamic movements of structural elements cause the deformation autowaves and autosolitons to propagate from the interfaces into blocks and along faults. Velocities of such deformation autowaves and autosolitons are low and proportional to velocities of the related movements of structural elements in the geomedium. Propagating in structural elements that are in a certain stress-strain state, deformation autowaves and autosolitons can be taken as small disturbances of the existing fields of the stress-strain state. A mathematical model is represented for the geomaterial treated as a nonequilibrium randomly inhomogeneous medium. Special features of the generation and propagation of deformation autosolitons in such media are studied

Dynamic Instability of Solid Surfaces under Load

International audienc

Dynamic Instability of Solid Surfaces under Load

International audienc