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The numerical solution of nonlinear problems on deformation and buckling of atomic lattices

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Abstract

The algorithm on numerical solution of problems on nonlinear deformation of atomic lattices is developed. The element of an atomic pair is implemented into the finite element library of PIONER code. The solution of the problem on quasistatic deformation and buckling of a four-atoms cell is presented. It follows from this solution that at stretching of the crystal, its buckling may be accompanied by occurrence of local shear bands.

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References

  • Bathe, K.-J. (1982). Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

  • Kaplan, I.G. (1982). Introduction to the Molecules Interactions, Science. Moscow, [in Russian].

  • Kornev, V.M. and Tikhomirov, Yu.V. (1993). The deformation and stability of the atomic chain at the tip of a crack. J. Appl. Mech. Techn. Phys. 34(3), 439-448.

    Article  Google Scholar 

  • Kornev, V.M. and Tikhomirov, Yu.V. (1994). On criteria of brittle fracture of solids with a crack accounting the atomic lattice defect. Mekhanika Tverdogo Tela 2, 185-193 [in Russian].

    Google Scholar 

  • Korobeinikov, S.N., Agapov, V.P., Bondarenko, M.I. and Soldatkin, A.N. (1989). The general purpose nonlinear finite element structural analysis program PIONER, Proc. Int. Conf. on Numerical Methods and Applications (Edited by B. Sendov et al.). Publ. House of the Bulgarian Acad. of Sci., Sofia, 228-233.

    Google Scholar 

  • Korobeinikov, S.N. (1997). Application of the FEMto solving nonlinear problems on deformation and buckling of atomic lattices, Preprint N0 1-97, Inst. Hydrodynamics, Sib. Div., Russ. Acad. of Sci., Novosibirsk [in Russian].

  • Korobeinikov, S.N. (2000). Nonlinear Strain Analysis of Solids. Publ. House of the Russian Acad. of Sci., Novosibirsk [in Russian].

    Google Scholar 

  • Novozhilov, V.V. (1969). To the bases of equilibrium cracks in elastic solids. Prikladnaja Matematika i Mekhanika 33(5), 797-812 [in Russian].

    Google Scholar 

  • Thompson, J.M.T. (1982). Bifurcational instability of an atomic lattice, Instabilities and Catastrophes in Science and Engineering (Edited by J.M.T. Thompson). Wiley, Chichester et al., 101-124.

    Google Scholar 

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  1. Lavrentiev Institute of Hydrodynamics, 630090, Novosibirsk, Russia

    S.N. Korobeinikov

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  1. S.N. Korobeinikov
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Korobeinikov, S. The numerical solution of nonlinear problems on deformation and buckling of atomic lattices. International Journal of Fracture 128, 315–323 (2004). https://doi.org/10.1023/B:FRAC.0000040995.13933.e0

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  • DOI: https://doi.org/10.1023/B:FRAC.0000040995.13933.e0

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