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Stochastic modeling of brittle fracture of materials with jerky crack dynamics

TitleStochastic modeling of brittle fracture of materials with jerky crack dynamics
AuthorsR. T. Sibatov1, 2, E. V. Morozova2, D. A. Timkaeva2
1Scientific Manufacturing Complex «Technological Centre»
2Ulyanovsk State University
AnnotationNumerous 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.
Keywordsbrittle fracture, random process, fractional derivative, Levy flights, intermittency.
CitationSibatov 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: 13.12.2024.