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IssuesArchive of Issues2005-1pp.72-85

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A. M. Krivtsov and V. P. Myasnikov, "Modeling of the change of the internal structure and stress state in a material subjected to high thermal loads on the basis of the particle dynamics method," Mech. Solids. 40 (1), 72-85 (2005)
Year 2005 Volume 40 Number 1 Pages 72-85
Title Modeling of the change of the internal structure and stress state in a material subjected to high thermal loads on the basis of the particle dynamics method
Author(s) A. M. Krivtsov (St. Petersburg)
V. P. Myasnikov (Moscow)
Abstract Irreversible changes in the internal structure occur in materials subjected to high-temperature loads. The description of such processes within the framework of continuum mechanics meets significant difficulties. These difficulties are associated with the fact that in the process of reconstruction of the internal structure of the material, the basic concept of the continuum mechanics - continuity of strains - is violated. In the present study, the particle dynamics (molecular dynamics) method is applied. This approach is essentially discrete and does not use the assumption of continuity. The solution is considered for a two-dimensional problem of change of the internal structure and appearance of the thermal stresses in a material subjected to high thermal load which is not uniform with respect to one of the spatial coordinates. As the initial material, we use an ideal crystal of particles interacting in accordance with the Lennard-Jones potential. It is shown that the characteristics of the internal structure substantially depend on the rate of cooling of the material. The effect of the character of the thermal load and defects of the internal structure on the residual stresses in the material is analyzed.
References
1.  V. A. Vinokurov, S. A. Kurkin, and G. A. Nikolaev. Welded Structures: Fracture Mechanics and Operability Criteria [in Russian], Mashinostroenie, Moscow, 1996.
2.  V. P. Myasnikov and M. A. Guzev, "Geometrical model of the structure of an elastoplastic continuum with defects," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, Vol. 40, No. 2, pp. 163-173, 1999.
3.  V. P. Myasnikov and M. A. Guzev, "Geometrical model of internal self-balanced stresses in solids," Doklady AN, Vol. 380, No. 5, pp. 427-429, 2001.
4.  R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles, A. Hilger, N.J., 1988.
5.  A. M. Krivtsov and N. V. Krivtsova, "The particle method and its application in solid mechanics," Dal'nevostochnyi Matem. Zh., Vol. 3, No. 2, pp. 254-276, 2002.
6.  M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1987.
7.  Yu. K. Tovbin (Editor), Molecular Dynamics Method in Physical Chemistry [in Russian], Nauka, Moscow, 1996.
8.  O. M. Belotserkovskii and Yu. M. Davydov, Particle-in-cell Method in Gas Dynamics [in Russian], Nauka, Moscow, 1982.
9.  A. M. Krivtsov and N. F. Morozov, "On the mechanical characteristics of nano-scale objects," Fizika Tverdogo Tela, Vol. 44, No. 12, pp. 2158-2163.
10.  A. M. Krivtsov, "To the theory of media with microstructure," in Trudy SPbGTU, No. 443, pp. 9-17, 1992.
11.  A. M. Krivtsov, "Constitutive equations for the nonlinear crystal lattice," ZAMM, Vol. 79, Sup. 2, pp. S419-S420, 1999.
Received 13 October 2003
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