International Conference «Mathematical and Informational Technologies, MIT-2013»

(X Conference «Computational and Informational Technologies for Science,

Engineering and Education»)

## Gerasimov A.V.## Numerical simulation of the failure of solids under intense dynamic loading
Under intensive dynamic loading in a solid produces a large number of cracks, leading to the formation of fragments of various shapes and sizes. Natural heterogeneity of the structure of materials affects the distribution of physical and mechanical characteristics of the material in terms of the body in question and consideration of this factor in the equations of solid mechanics is only possible with a random distribution of the strength properties of the initial deviations from the nominal value. Parameters such as yield strength, tensile strength, maximum strain and other constants that define the time of the destruction in various theories of strength and failure criteria are directly dependent on the number and size of defects, and must be dispersed in a random manner, with a variance that depends on the uniformity of material. Therefore, in mathematical analysis of the fragmentation of real materials must take into account the distribution of the initial inhomogeneities and make some disturbance in the physical and mechanical characteristics of the destroyed environment for the adequacy of the numerical calculations with experimental data. In this case, the physical and mechanical characteristics of the environment are responsible for the strength, considered to be distributed randomly over the volume of the material, and the process of destruction becomes probabilistic, which corresponds to the theoretical and experimental data.
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