The problem of obtaining nano- particles (NP) and producing materials on their basis has recently become especially urgent. Using UDP and clusters is effective in mechanical and instrument engineering, energetic, micro electronics, computer engineering, geology, medicine, agriculture and other fields. In this connection the task of NP production methods development becomes urgent. It will be noted that the physics of these processes, the development of new highly productive and economically profitable methods of NP obtaining requires substantial material resources. Hence the application of mathematical modelling methods allowing to carry out prior investigations of NP formation processes and to save time and economize resources while developing new technologies is quite necessary.
The problem of modelling of the nano size powder materials manufacturing processes should be considered on different structural levels in the process of the particle size reduction. The first level of modelling corresponds the dimensions of the structural elements of the material (grains, dendrite crystals and so on) being one or two orders smaller than the particle size. This is due to the statistic distribution of the axis orientation of the separate crystals isotropy. On reducing the dimensions of the particle up to the value comparable with a characteristic size of a structural element the influence of the space structure of the material essentially increases. However, even on this level modelling of the particles dispersion process can be carried out within the limits of phenomenological equations of the mechanics of continuous medium, as the dimensions of elementary cells of a crystalline lattice are much smaller than the sizes of the grain. On further reducing the particle size namely up to the order of < 10 nm the structure of the crystalline lattice of the material acquires great importance. Modelling the dispersion process in a given spacious size within the phenomenological description by the model of continuous medium is not quite correct as it doesn't reflect the essence of the physical processes taking place on the structural level considered. The mathematical model of the particles formation process in this case should be based on the theory of the inter atomic interaction within the potential theory limits.
The purpose of this work was the development of task formulation and numerical research of dynamic rupture problem of the powder materials up to the nano - particles under the impact power influence [1-3].
Vakhrouchev A. V., Lipanov A.M. A numerical analysis of the rupture of powder materials under the power impact influence.-Computer & Structures, v.44,N1/2,pp.481-486,1992.
Vakhrouchev A. V., Lipanov A.M. "The numerical simulation of the cluster static and dynamics", The proceeding of the international conference, "Application of the mathematics modeling in the science and techniques", Izhevsk, p.p. 158-163,1996 (in Russian).
Vakhrouchev A.V., Lipanov A.M. A numerical modelling of powder particles micro-mechanics rupture. - Abstracts 1st El.B.A. Foresights Forum on nanotechnology. Rome p.67,1999.
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