Geodesic
Cellular automaton simulation of the fracture process for brittle materials
Prikladnaâ diskretnaâ matematika, no. 2 (2015), pp. 103-117

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A three-dimensional probabilistic cellular automaton is constructed to simulate the evolution of cluster structure of elementary damages in loaded materials. The comparison of the statistical characteristics of time series “number of clusters” and “number of elementary damages” are made for three-dimensional and two-dimensional cellular automata. It is shown, that the transition of the time autocorrelation function of a random process “number of elementary damages” to the range of negative correlations and the emergence of the second linear portion on the statistics of the normalized Hurst's range can be interpreted as presages of material transition to the stage preceding to complete destruction. It is found that, for the three-dimensional model based on the value of probability of damage cluster perimeter germination, there are two qualitatively different modes of damage accumulation.
Keywords: cellular automaton, damage clusters, fracture prediction. 
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     author = {D. V. Alekseev and G. A. Kazunina and A. V. Cherednichenko},
     title = {Cellular automaton simulation of the fracture process for brittle materials},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {103--117},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2015_2_a10/}
}
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D. V. Alekseev; G. A. Kazunina; A. V. Cherednichenko. Cellular automaton simulation of the fracture process for brittle materials. Prikladnaâ diskretnaâ matematika, no. 2 (2015), pp. 103-117. http://geodesic.mathdoc.fr/item/PDM_2015_2_a10/