Far Eastern Mathematical Journal

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Method of particles and its application to mechanics of solids


A. M. Krivtsov, N. V. Krivtsova

2002, issue 2, P. 254–276


Abstract
The basics of the particles dynamic method are presented as well as applications of this method to mechanics of solids. Different potentials of interaction are described. The parameters characterizing the laws of interaction are outlined. The main principles for setting correspondence between the microparameters of the simulation and the macroparameters of the object being modeled are described.

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References

[1] M. P. Allen and A. K. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1987.
[2] W. G. Hoover, Isomorphism linking smooth particles and embedded atoms, Physica A, 260:3-4 (199.
[3] A. V. Zabrodin, Super E'VM MVS-100, MVS-1000 i opyt ix ispol'zovaniya pri reshenii zadach mexaniki i fiziki, Matematicheskoe modelirovanie, 12:5 (2000), 61–66.
[4] S. Nose, Constant-Temperature Molecular-Dynamics, Journal of Physics – Condensed Matter, 2 (1990), 115–119.
[5] L. Verlet, Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev., 159 (1967), 98–103.
[6] J. B. Gibson, A. N. Goland, M. Milgram and G. H. Vineyard, Phys. Rev., 120 (1960), 1229.
[7] A. Nordsieck, Math. Comput., 16 (1962), 22.
[8] S. Erkoc, Empirical many-body potential energy functions used in computer simulations of condensed matter properties, Physics Reports, 278:2 (1997), 80–105.
[9] A. M. Krivtsov, Second Order Equation of State for Lennard-Jones Chain, Proceedings of the XXVIII Summer School Actual Problems in Mechanics, 1, St.-Petersburg. Russia, 2001, 79–90.
[10] N. J. Wagner, B. L. Holian, A. F. Voter, Molecular-Dynamics Simulations of 2-Dimensional Materials at High-Strain Rates, Physical Review A, 45:12 (1992), 8457–8470.
[11] V. A. Lagunov, A. B. Sinani, Obrazovanie bistruktury tverdogo tela v komp'yuternom e'ksperimente, Fizika tverdogo tela, 40:10 (1998), 1919–1924.
[12] A. M. Krivcov, K teorii sred s mikrostrukturoj, Tr. SPbGTU, 443, 1992, 9–17.
[13] A. M. Krivtsov, Constitutive Equations of the Nonlinear Crystal Lattice, ZAMM, 79:2 (1999), 419–420.
[14] U. Vuster, Primenenie tenzorov i teorii grupp dlya opisaniya fizicheskix svojstv kristallov, Mir, M., 1977.

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