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IssuesArchive of Issues2010-3pp.352-369

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B.D. Annin, V.V. Alekhin, A.V. Babichev, and S.N. Korobeynikov, "Computer Simulation of Nanotube Contact," Mech. Solids. 45 (3), 352-369 (2010)
Year 2010 Volume 45 Number 3 Pages 352-369
DOI 10.3103/S0025654410030064
Title Computer Simulation of Nanotube Contact
Author(s) B.D. Annin (Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, pr-t akad. Lavrentyeva 15, Novosibirsk, 630090 Russia, annin@hydro.nsc.ru)
V.V. Alekhin (Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, pr-t akad. Lavrentyeva 15, Novosibirsk, 630090 Russia, alekhin@hydro.nsc.ru)
A.V. Babichev (Sobolev Institute of Geology and Mineralogy, Siberian Branch of Russian Academy of Sciences, pr-t akad. Koptyuga 3, Novosibirsk, 630090 Russia, babichev@uiggm.nsc.ru)
S.N. Korobeynikov (Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, pr-t akad. Lavrentyeva 15, Novosibirsk, 630090 Russia, S.N.Korobeynikov@mail.ru)
Abstract We develop procedures of numerical solution of nanostructure contact problems, which are based on the time discretization of nonlinear equations of molecular mechanics. The matrices and vectors of these equations are determined by using the Morse law of covalent atomic interaction, the fictitious rod elements to take account of angular variations between neighboring atomic covalent bonds, and noncovalent Van der Waals forces to take account of contact interactions between the graphene-like nanostructures. The procedures developed were included into the computational package PIONER, which was used to solve the problem of contact/self-contact of two nanotubes under conditions of dynamic equilibrium. We showed that the type of contact interaction significantly depends on the impact velocity of nanotubes. For a relatively small impact velocity, the nanotubes "adhere" to each other with a small deformation of their walls, due to the action of the Van der Waals attractive forces. As the impact velocity increases, the nanotubes fly apart because of the action of noncovalent repulsive forces. As the impact velocity continues to increase, there is a strong deformation of nanotubes with instantaneous "adhesion" of opposite ends and further separation of tubes. We show that taking account of the noncovalent forces of interaction between the opposite parts of the nanotube walls prevents their self-intersection; in this region of the nanotube contact, ovalization of their transverse cross-sections occurs.
Keywords nanotube, contact, Van der Waals forces, molecular mechanics
References
1.  K. Ariga and T. Kunitake, Supramolecular Chemistry - Fundamentals and Applications (Springer, Berlin, 2006).
2.  M. J. Buehler, Atomic Modeling of Materials Failure (Springer, New York, 2008).
3.  W. K. Liu, E. G. Karpov, and H. S. Park, Nano Mechanics and Materials: Theory, Multiscale Methods and Applications (Wiley, Chichester, 2006).
4.  H. Ralf-Tabar, Computational Physics of Carbon Nanotubes (Cambridge Univ. Press, Cambridge, 2008).
5.  B. I. Yakobson and L. S. Couchman, Nanotubes: Supramolecular Mechanics in Dekker Encyclopedia of Nanoscience and Nanotechnology (Marcel Dekker, New York, 2004).
6.  J. Z. Zhang, Z. L. Wang, J. Liu, et. al., Self-Assembled Nanostructures (Kluwer Acad. Publ., New York, 2004).
7.  M. Arroyo and T. Belytschko, "Finite Element Methods for the Non-Linear Mechanics of Crystalline Sheets and Nanotubes," Int. J. Numer. Meth. Engng 59 (3), 419-456 (2004).
8.  R. C. Batra and A. Sears, "Continuum Model of Multi-Walled Carbon Nanotubes," Int. J. Solids Struct. 44, 7577-7596 (2007).
9.  N. Hu, K. Nunoya, D. Pan, et al., "Prediction of Buckling Characteristics of Carbon Nanotubes," Int. J. Solids Struct. 44 (20), 6535-6550 (2007).
10.  A. L. Kalamkarov, A. V. Georgiades, S. K. Rokkam, et al., "Analytical and Numerical Techniques to Predict Carbon Nanotubes Properties," Int. J. Solids Struct. 43 (22/23), 6832-6854 (2006).
11.  A. Y. T. Leung, X. Guo, and X. Q. He, "Postbuckling of Carbon Nanotubes by Atomic-Scale Finite Element," J. Appl. Phys. 99, p. 124308 (2006).
12.  R. Saito, R. Matsuo, T. Kimura, et al., "Anomalous Potential Barrier of Double-Wall Carbon Nanotube," Chem. Phys. Lett. 348 (3), 187-193 (2001).
13.  A. Sears and R. C. Batra, "Buckling of Multiwalled Carbon Nanotubes under Axial Compression," Phys. Rev. B 73 (8), 085410 (2006).
14.  H. S. Shen and C. L. Zhang, "Postbuckling Prediction of Axially Loaded Double-Walled Carbon Nanotubes with Temperature Dependent Properties and Initial Defects," Phys. Rev. B 74 (3), 035410 (2006).
15.  Y. Y. Zhang, V. B. C. Tan, and C. M. Wang, "Effect of Strain Rate on the Buckling Behavior of Single- and Double-Walled Carbon Nanotubes," Carbon 45 (3), 514-523 (2007).
16.  H. W. Zhang, L. Wang, and J. B. Wang, "Computer Simulation of Buckling Behavior of Double-Walled Carbon Nanotubes with Abnormal Interlayer Distances," Comput. Mater. Sci. 39 (3), 664-672 (2007).
17.  S. Zhang, S. L. Mielke, R. Khare, et al., "Mechanics of Defects in Carbon Nanotubes: Atomic and Multiscale Simulation," Phys. Rev. B 71 (11), 115403 (2005).
18.  M. J. Buehler, Y. Kong, H. Gao, and Y. Huang, "Self-Folding and Unfolding of Carbon Nanotubes," Trans. ASME. J. Engng Mater. Technol. 128 (3), 3-10 (2006).
19.  M. Arroyo and T. Belytschko, "A Finite Deformation Membrane Based on Inter-Atomic Potentials for the Transverse Mechanics of Nanotubes," Mech. Mater. 35 (3), 193-215 (2003).
20.  G. Gao, T. Cagin, and W. A. Goddard III, "Energetics, Structure, Mechanical and Vibrational Properties of Single Walled Carbon Nanotubes," Nanotech. 9 (3), 184-191 (1998).
21.  B. Liu, H. Jiang, Y. Huang, et al., "Atomic-Scale Finite Element Method in Multiscale Computation with Applications to Carbon Nanotubes," Phys. Rev. B 72, 035435 (2005).
22.  S. J. V. Frankland, V. M. Harik, G. M. Odegard, et al., "The Stress-Strain Behavior of Polymer-Nanotube Composites from Molecular Dynamics Simulation," Compos. Sci. Technol. 63, 1655-1661 (2003).
23.  R. V. Goldstein and A. V. Chentsov, "Discrete-Continuous Model of a Nanotube," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 57-74 (2005) [Mech. Solids (Engl. Transl.) 40 (4), 45-59 (2005)].
24.  R. V. Goldstein, A. V. Chentsov, R. M. Kadushnikov, and N. A. Shturkin, "Methodology and Metrology for Mechanical Testing of Nano- and Microdimensional Objects, Materials, and Products of Nanotechnology," Ross. Nanotekhnol. 3 (1-2), 114-124 (2008) [Nanotechnol. Russ. (Engl. Transl.) 3 (1-2), 112-121 (2008)].
25.  N. Hu, H. Fukanaga, C. Lu, et al., "Prediction of Elastic Properties of Carbon Nanotube Reinforced Composites," Proc. Roy. Soc. London. Ser. A 461 (2058), 1685-1710 (2005).
26.  C. Y. Li and T. W. Chou, "Modeling of Carbon Nanotubes and Their Composites," in Nanomechanics of Materials and Structures (Springer, Berlin, 2006).
27.  G. M. Odegard, T. S. Gates, L. M. Nicholson, and E. Wise, "Equivalent-Continuum Modeling of Nano-Structured Materials," Compos. Sci. Technol. 62 (14), 1869-1880 (2002).
28.  Q. Wang, "Torsional Instability of Carbon Nanotubes Encapsulating C60 Fullerens," Carbon 47 (2), 507-512 (2009).
29.  N. G. Chopra, L. X. Benedict, V. H. Crespi, et al., "Fully Collapsed Carbon Nanotubes," Nature 377, 135-138 (1995).
30.  A. M. Krivtsov, Strain and Failure of Rigid Bodies with Microstructure (Fizmatlit, Moscow, 2007) [in Russian].
31.  T. S. Gates, G. M. Odegard, S. J. V. Frankland, and T. C. Clancy, "Computational Materials: Multi-Scale Modeling and Simulation of Nanostructured Materials," Compos. Sci. Technol. 65 (15/16), 2416-2434 (2005).
32.  S. N. Korobeynikov, "Nonlinear Equations of Deformation of Atomic Lattices," Arch. Mech. 57 (6), 457-475 (2005).
33.  B. D. Annin, S. N. Korobeynikov, and A. V. Babichev, "Computer Simulation of a Twisted Nanotube Buckling," Sib. Zh. Industr. Mat. 11 (1), 3-22 (2008) [J. Appl. Industr. Math. (Engl. Transl.) 3 (3), 318-333 (2009)].
34.  S. N. Korobeynikov, "The Numerical Solution of Nonlinear Problems on Deformation and Buckling of Atomic Lattices," Int. J. Fract. 128 (1), 315-323 (2004).
35.  S. N. Korobeynikov and A. V. Babichev, "Numerical Simulation of Dynamic Deformation and Buckling of Nanostructures," in CD ICF Interquadrennial Conference Full Papers (Institute for Problems in Mechanics, Moscow, 2007).
36.  S. N. Korobeynikov and A. V. Babichev, "Nanotube Buckling under Sudden Application of Axial Load," in Mathematical Modeling of Systems and Processes (Izd-vo PGTU, Perm, 2008), pp. 43-54 [in Russian].
37.  K. M. Liew, C. H. Wong, and M. J. Tan, "Tensile and Compressive Properties of Carbon Nanotube Bundles," Acta Mater. 54 (1), 225-231 (2006).
38.  C.-L. Zhang and 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).
39.  M. Arroyo and T. Belytschko, "Finite Crystal Elasticity of Carbon Nanotubes Based on the Exponential Cauchy-Born Rule," Phys. Rev. B 69, 115415 (2004).
40.  B. Liu, Y. Huang, H. Jiang, et al., "The Atomic-Scale Finite Element Method," Comput. Methods Appl. Mech. Engng 193 (17-20), 1849-1864 (2004).
41.  N. A. Kasti, "Zigzig Carbon Nanotubes - Molecular/Structural Mechanics and Finite Element Method," Int. J. Solids Struct. 44, 6914-6929 (2007).
42.  A. Y. T. Leung, X. Guo, X. Q. He, and S. Kitipornchai, "A Continuum Model for Zigzag Single-Walled Carbon Nanotubes," Appl. Phys. Lett. 86, 083110 (2005).
43.  C. Y. Li and T. W. Chou, "A Structural Mechanics Approach for the Analysis of Carbon Nanotubes," Int. J. Solids Struct. 40 (10), 2487-2499 (2003).
44.  Y. Wang, C. Sun, X. Sun, et al., "2-D Nano-Scale Finite Element Analysis of a Polymer Field," Compos. Sci. Technol. 63, 1581-1590 (2003).
45.  H. W. Zhang, L. Wang, J. B. Wang, and H. F. Ye, "Parametric Variational Principle and Quadratic Programming Method for van der Waals Force Simulation of Parallel and Cross Nanotubes," Int. J. Solids Struct. 44 (9), 2783-2801 (2007).
46.  H. W. Zhang, Z. Yao, J. B. Wang, and W. X. Zhong, "Phonon Dispersion Analysis of Carbon Nanotubes Based on Inter-Belt Model and Symplectic Solution Method," Int. J. Solids Struct. 44 (20), 6428-6449 (2007).
47.  MARC Users Guide, Vol. C: Program Input (MSC.Software Corporation, Santa Ana, 2007).
48.  L. A. Girifalco, M. Hodak, and R. S. Lee, "Carbon Nanotubes, Buckyballs, Ropes, and a Universal Graphitic Potential," Phys. Rev. B 62 (19), 13104-13110 (2000).
49.  A. S. Kravchuk, "On Models and Solution of Problems of Nanocontact Mechanics," in Mathematical Modeling of Systems and Processes (Izd-vo PGTU, Perm, 2007), pp. 123-141 [in Russian].
50.  S. N. Korobeynikov, Nonlinear Strain of Rigid Bodies (Sib. otdel. RAN, Novosibirsk, 2000) [in Russian].
51.  S. N. Korobeynikov, V. P. Agapov, M. I. Bondarenko, and A. N. Soldatkin, "The General Purpose Nonlinear Finite Element Structural Analysis Program PIONER," in Proc. Int. Conf. Numerical Methods and Applications (Publ. House of the Bulgarian Acad. of Sci., Sofia, 1989), pp. 228-233.
52.  S. B. Sinnott, O. A. Shenderova, C. T. White, and D. W. Brenner, "Mechanical Properties of Nanotubule Fibers and Composites Determined from Theoretical Calculations and Simulations," Carbon 36 (1-2), 1-9 (1998).
53.  PATRAN Users Guide (MSC.Software Corporation, Santa Ana, 2007).
54.  A. V. Babichev, "Automating Model Construction and Visualization of Results of Numerical Simulation of Deformation of Nanostructures," Vych. Mekh. Sploshn. Sred 1 (4), 21-27 (2008).
55.  E. G. Rakov, Nanotubes and Fullerens (Logos, Moscow, 2006) [in Russian].
56.  T. Belytschko, S. P. Xiao, G. C. Schatz, and R. S. Ruoff, "Atomic Simulations of Nanotube Fracture," Phys. Rev. B 65, 235430 (2002).
Received 29 January 2010
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