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