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Stochastic modeling of brittle fracture of materials with jerky crack dynamics
| Title | Stochastic modeling of brittle fracture of materials with jerky crack dynamics |
|---|---|
| Authors | R. T. Sibatov1, 2, E. V. Morozova2, D. A. Timkaeva2 1Scientific Manufacturing Complex «Technological Centre» 2Ulyanovsk State University |
| Annotation | Numerous experiments have demonstrated that brittle fracture of materials exhibits scale-invariant properties. There is a jerky dynamics of cracks with random impulsive energy releases. The energies of these individual events follow a power law distribution, covering a wide range of values. A stochastic process has been proposed to describe brittle fracture of materials with scale-invariant properties, representing a mixture of the Ornstein–Uhlenbeck process and one-sided Levy flights. The former corresponds to a Poisson flow of degradation events, while the latter describes the intermittent dynamics of crack growth. The flow of crack length increment events is governed by a fractional Poisson process, and the contribution of these events to the failure of the system follows a power law distribution. A criterion has been proposed to predict the guaranteed service life of the material without failure. |
| Keywords | brittle fracture, random process, fractional derivative, Levy flights, intermittency. |
| Citation | Sibatov R. T., Morozova E. V., Timkaeva D. A. ''Stochastic modeling of brittle fracture of materials with jerky crack dynamics'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 188-192. Available at: https://conf.svmo.ru/files/2024/papers/paper35.pdf. - Date of access: 21.11.2024. |
© SVMO, National Research Mordovia State University, 2024
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