A probabilistic approach to modeling collisions with thin barriers

Abstract

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 us to model structural heterogeneities of the material in a simple form, practically without any 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 number and size of the “petals” at the penetration of thin barriers depend of the speed of the projectile and the strength characteristics of the barrier.

Probabilistic approach in modelling dynamic fracture problems

“…In the probability theory, this directly corresponds to the law of normal distribution. This paper, in contrast to the works 10,[13][14][15] that use the Weibull distribution, proposes to use the normal (Gaussian) distribution as theoretically justified and more convenient for simulation.…”

“…For numerical simulation of fragmentation problems, regardless of whether the mesh or meshless method is used (SPH method 17 ), the material is represented by a model with discrete parameters relative to computational nodes and cells. 10 To simulate an inhomogeneous structure, the initial distribution of strength material characteristics should be changed in the proposed probabilistic approach. This paper proposes to modify the initial distribution of yield strength and fracture criterion.…”

“…The process of fracture and fragmentation of deformable bodies is probabilistic, which is determined by the stochastic distribution of defects and inhomogeneities in the structure of the material. 9,10 The most obvious probabilistic nature of fragmentation was demonstrated experimentally and numerically for the fracture of cylindrical shells under explosive loading. [11][12][13] The initial loading conditions in this case have axial symmetry; however, during loading, deformations are concentrated in the inhomogeneities of the material structure.…”