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Stability/instability criteria of discrete elastic systems are used to study the buckling of nanostructures. The deformation of nanostructures is simulated by solving the nonlinear equations of molecular mechanics. The external forces applied to the nanostructure are assumed to be dead (that is the directions of their action remain constant throughout nanostructure deformation). We note that the positive-definiteness property of the tangential stiffness matrix of a nanostructure is a universal sufficient stability criterion for both equilibrium states and quasi-static/dynamic motions of the nanostructure. The equilibrium configurations are stable in Lyapunov's sense, and quasi-static/dynamic motions are stable in a finite time interval t "isin" (0, Tcr) in which the positive-definiteness property of this matrix is preserved. For dynamic motions of nanostructures, the stability property in this time interval follows from Lee’s criterion of quasi-bifurcation of solutions of second order ODEs. The non-positive definiteness of the tangential stiffness matrix of nanostructures at a time t > Tcr corresponds to both unstable equilibrium configurations and unstable dynamic motions. Computer procedures for determining the critical time and buckling mode(s) are developed using this criterion and are implemented in the PIONER FE code. This code is used to obtain new solutions for the deformation and buckling of twisted (10, 10) armchair and (10, 0) zigzag single-walled carbon nanotubes
Czasopismo
Rocznik
Tom
Strony
367--404
Opis fizyczny
Bibliogr. 51 poz.
Twórcy
autor
autor
autor
autor
- Lavrentyev Institute of Hydrodynamics Lavrentyev av., 15 and Novosibirsk State University Pirogova str., 2, Novosibirsk, 630090, Russia, s.n.korobeynikov@mail.ru
Bibliografia
- 1. B.D. Annin, S.N. Korobeynikov, A.V. Babichev, Computer simulation of a twisted nanotube buckling, J. Appl. Ind. Math., 3, 3, 318–333, 2009.
- 2. B.D. Annin, V.V. Alekhin, A.V. Babichev, S.N. Korobeynikov, Computer simulation of nanotube contact, Mech. Solids, 45, 3, 352–369, 2010.
- 3. R. Ansari, S. Rouhi, Atomistic finite element model for axial buckling of single-walled carbon nanotubes, Physica E, 43, 58–69, 2010.
- 4. M. Arroyo, T. Belytschko, An atomistic-based finite deformation membrane for single layer crystalline films, J. Mech. Phys. Solids, 50, 1941–1977, 2002.
- 5. M. Arroyo, T. Belytschko, A finite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes, Mechanics of Materials, 35, 3–6, 193–215, 2003.
- 6. A.V. Babichev, Automating model construction and visualization of results of numerical simulation of deformation of nanostructures, Comp. Cont. Mech., 1, 4, 21–28, 2008 [In Russian].
- 7. K.-J. Bathe, Finite Element Procedures, Prentice Hall, Upper Saddle River, New Jersey, 1996.
- 8. R.C. Batra, S.S. Gupta, Wall thickness and radial breathing modes of single-walled carbon nanotubes, Trans. ASME. J. Appl. Mech., 75, 061010, 2008.
- 9. T. Belytschko, S.P. Xiao, G.C. Schatz, R.S. Ruoff, Atomistic simulations of nanotube fracture, Phys. Rev. B, 65, 235430, 2002.
- 10. N.G. Chopra, L.X. Benedict, V.H. Crespi, M.L. Cohen, S.G. Louie, A. Zettl, Fully collapsed carbon nanotubes, Nature, 377, 135–138, 1995.
- 11. A. Curnier, Computational Methods in Solid Mechanics, Kluwer Academic Publ., Dordrecht, 1994.
- 12. P. Dłużewski, P. Traczykowski, Numerical simulation of atomic positions in quantum dot by means of molecular statics, Arch. Mech., 55, 5–6, 393–406, 2003.
- 13. C.L. Dym, Stability Theory and Its Applications to Structural Mechanics, Noordhoff Int. Publ., Leyden 1974.
- 14. L.A. Elsgolts, Differential Equations and Variational Calculus, Nauka, Moscow 1969 [in Russian].
- 15. L.A. Girifalco, M. Hodak, R.S. Lee, Carbon nanotubes, buckyballs, ropes, and a Universal graphitic potential, Phys. Rev. B, 62, 19, 13104–13110, 2000.
- 16. R.V. Goldstein, A.V. Chentsov, A discrete-continuous model of a nanotube, Mech. Solids, 40, 4, 45–59, 2005.
- 17. R.V. Goldstein, A.V. Chentsov, R.M. Kadushnikov, N.A. Shturkin, Methodology and metrology for mechanical testing of nano-and microdimensional objects, materials, and products of nanotechnology, Nanotechnologies in Russia, 3, 1–2, 112–121, 2008.
- 18. S.S. Gupta, R.C. Batra, Elastic properties and frequencies of free vibrations of singlelayer graphene sheets, Journal of Computational and Theoretical Nanoscience, 7, 1–14, 2010.
- 19. N. Hu, K. Nunoya, D. Pan, T. Okabe, H. Fukanaga, Prediction of buckling characteristics of carbon nanotubes, Int. J. Solids Structures, 44, 20, 6535–6550, 2007.
- 20. X. Huang, H. Yuan, W. Liang, S. Zhang, Mechanical properties and deformation morphologies of covalently bridged multi-walled carbon nanotubes: Multiscale modeling, J. Mech. Phys. Solids, 58, 1847–1862, 2010.
- 21. Z. Kang, M. Li, Q. Tang, Buckling behavior of carbon nanotube-based intramolecular junctions under compression: Molecular dynamics simulation and finite element analysis, Computational Materials Science, 50, 253–259, 2010.
- 22. A.R. Khoei, E. Ban, P. Banihashemi, M.J. Abdolhosseini Qomi, Effects of temperature and torsion speed on torsional properties of single-walled carbon nanotubes, Materials Science and Engineering C, 31, 452–457, 2011.
- 23. M. Kleiber, W. Kotula, M. Saran, Numerical analysis of dynamic quasi-bifurcation, Engineering Computations, 4, 1, 48–52, 1987.
- 24. S.N. Korobeinikov, V.P. Agapov, M.I. Bondarenko, A.N. Soldatkin, The general purpose nonlinear finite element structural analysis program PIONER, [in:] B. Sendov et al. [Eds.], Proc. Int. Conf. on Numerical Methods and Applications, Publ. House of the Bulgarian Acad. of Sci., Sofia, pp. 228–233, 1989.
- 25. S.N. Korobeynikov, Application of finite element method for solving the nonlinear problems on deformation and buckling of atomic lattices, Lavrentyev Institute of Hydrodynamics, Novosibirsk, Preprint No. 1-97, 1997 [in Russian].
- 26. S.N. Korobeinikov, The numerical solution of nonlinear problems on deformation and buckling of atomic lattices, Int. J. Fracture, 128, 1, 315–323, 2004.
- 27. S.N. Korobeynikov, Nonlinear equations of deformation of atomic lattices, Arch. Mech., 57, 6, 457–475, 2005.
- 28. S.N. Korobeynikov, A.V. Babichev, Numerical simulation of dynamic deformation and buckling of nanostructures, [in:] R.V. Goldstein [Ed.], CD ICF Interquadrennial conference full papers, Moscow, Russia, 7–12 July, 2007, Institute for Problems in Mechanics, Moscow 2007.
- 29. W.B. Krätzig, L.-Y. Li, On rigorous stability conditions for dynamic quasi-bifurcations, Int. J. Solids Structures, 29, 1, 97–104, 1992.
- 30. W.B. Krätzig, P. Nawrotzski, P. Wriggers, S. Reese, Fundamentals of nonlinear instabilities and response analysis of discretized systems, [in:] A.N. Kounadis, W.B. Krätzig [Eds.], Nonlinear Stability of Structures (Theory and Computation Techniques), CISM Courses and Lectures No. 342, Springer, Wien, pp. 245–415, 1995.
- 31. A.M. Krivtsov, Deformation and Failure of Solids with Microstructure, Fizmatlit, Moscow 2007 [in Russian].
- 32. J. La Salle, S. Lefschetz, Stability by Liapunov’s Direct Method with Applications, Academic Press, New York, London 1961.
- 33. L.H.N. Lee, On dynamic stability and quasi-bifurcation, Int. J. Non-Linear Mech., 16, 1, 79–87, 1981.
- 34. A.Y.T. Leung, X. Guo, X.Q. He, H. Jiang, Y. Huang, Postbuckling of carbon nanotubes by atomic-scale finite element, J. Appl. Phys., 99, 124308, 2006.
- 35. C. Li, T.W. Chou, A structural mechanics approach for the analysis of carbon nanotubes, Int. J. Solids Structures, 40, 2487–2499, 2003.
- 36. B. Liu, Y. Huang, H. Jiang, S. Qu, K.C. Hwang, The atomic-scale finite element method, Comput. Methods Appl. Mech. Engrg., 193, 1849–1864, 2004.
- 37. B. Liu, H. Jiang, Y. Huang, S. Qu, M.-F. Yu, Atomic-scale finite element method in multiscale computation with applications to carbon nanotubes, Phys. Rev. B, 72, 035435, 2005.
- 38. G.M. Odegard, T.S. Gates, L.M. Nicholson, E.Wise, Equivalent-continuum modeling of nano-structured materials, Composites Science and Technology, 62(14), 1869–1880, 2002.
- 39. V. Parvaneh, M. Shariati, A.M.M. Sabeti, Investigation of vacancy defects effects on the buckling behavior of SWCNTs via a structural mechanics approach, European Journal of Mechanics A/Solids, 28, 1072–1078, 2009.
- 40. R. Saito, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Electronic structure of chiral graphene tubules, Appl. Phys. Lett. 60, 18, 2204–2206, 1992.
- 41. A. Sakhaee-Pour, Elastic buckling of single-layered graphene sheet, Computational Materials Science, 45, 266–270, 2009.
- 42. A.R. Setoodeh, M. Jahanshahi, H. Attariani, Atomistic simulations of the buc kling behavior of perfect and defective silicon carbide nanotubes, Computational Materials Science, 47, 388–397, 2009.
- 43. A. Shahabi, M. Ghassemi, S.M. Mirnouri Langroudi, H. Rezaei Nejad, M.H. Hamedi, Effect of defect and C60s density variation on tensile and compressive properties of peapod, Computational Materials Science, 50, 586–594, 2010.
- 44. V.I. Shalashilin, E.B. Kuznetsov, Parametric Continuation and Optimal Parametrization in Applied Mathematics and Mechanics, Kluwer Academic Publ., Dordrecht 2003.
- 45. T. Sokol, M. Witkowski, The equilibrium path determination in nonlinear analysis of structures, [in:] M. Papadrakakis, B.H.V. Topping [Eds.], Advances in Non-linear Finite Element Methods: Proc. 2nd Int. Conf. on Computational Structures Technology, Civil-Comp Press, Edinburgh, pp. 35–45, 1994.
- 46. H.Y. Song, X.W. Zha, Molecular dynamics study of effects of nickel coating on torsional behavior of single-walled carbon nanotube, Physica B, 406, 992–995, 2011.
- 47. J. Wackerfuß, Molecular mechanics in the context of the finite element method, Int. J. Num. Meth. Engng, 77, 969–997, 2009.
- 48. C.M. Wang, Y.Y. Zhang, Y. Xiang, J.N. Reddy, Recent studies on buckling of carbon nanotubes, Appl. Mech. Reviews, 63, 030804, 2010.
- 49. Z. Wang, D. Cheng, Z. Li, X. Zu, Atomistic simulation of the torsional buckling of single-crystalline GaN nanotubes, Physica E, 41, 88–91, 2008.
- 50. Z. Waszczyszyn, C. Cichoń, M. Radwańska, Stability of Structures by Finite Element Method, Elsevier, Amsterdam 1994.
- 51. C.-L. Zhang, H.-S. Shen, Buckling and postbuckling analysis of single-walled carbon nanotubes in thermal environments via molecular dynamics simulation, Carbon, 44, 13, 2608–2616, 2006.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0012-0054