Pashkov S.V.  

Probabilistic approach in modeling dynamic fracture problems

In many fracture problems, fragmentation is essentially a probabilistic process, which is determined by the stochastic nature of the distribution of inhomogeneities of the internal structure of material. The probabilistic approach is described, which allows to model structural heterogeneities of the material in a simple form, practically without complication of the model and additional experiments.
Using experimental data and numerical simulation results, it is shown, that the introduction of only one additional parameter (dispersion of the strength properties distribution) into the material model makes it possible to give a probabilistic character to the crack formation process at any scale level, which corresponds to theoretical concepts and experimental data.
Distribution of materials strength characteristics (according to the selected distribution law) in the cells of the computational domain is used for initial heterogeneities and materials structure defects modeling. It is shown that the fragmentation spectra obtained using different distribution laws with the same dispersion coincide up to the probability factor, which allows to use any distribution law in the calculations.

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