The molecular dynamic finite element method (MDFEM)

Computers, Materials and Continua

Volumn 19, Issue 1, 2010, Pages 57-104

  Nasdala, Lutz ^a   Kempe, Andreas ^a   Rolfes, Raimund ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

Carbon nanotubes; Continuum mechanics; Elastomeric material; Force fields; Molecular dynamic finite element method (MDFEM); Particle mechanics

Indexed keywords

AIRCRAFT PANELS; ATOMIC INTERACTIONS; CLASSICAL MOLECULAR DYNAMICS; CONFORMATIONAL ANALYSIS; DYNAMIC FINITE ELEMENT METHOD; ELASTOMERIC MATERIALS; ENGINEERING STRUCTURES; EQUILIBRIUM CONFIGURATION; FINITE ELEMENT; FORCE FIELDS; FRICTIONAL CONTACT; INELASTIC MATERIALS; MACRO SCALE; MATERIAL PARAMETER; MD SIMULATION; MOLECULAR DYNAMIC FINITE ELEMENT METHOD (MDFEM); MOLECULAR SCALE; MULTI-BODY; NATURAL LENGTH; NONLINEAR SURFACE; PARTICLE MECHANICS; ROTATIONAL DEGREES OF FREEDOM; UNDERLYING MECHANISM; VEHICLE CHASSIS;

ATOMS; CARBON NANOTUBES; CONTINUUM MECHANICS; DYNAMICS; ELASTICITY; ELASTOMERS; MATERIALS; MECHANISMS; MOLECULAR DYNAMICS;

FINITE ELEMENT METHOD;

EID: 79951992813     PISSN: 15462218     EISSN: 15462226     Source Type: Journal    
DOI: None     Document Type: Article

References (49)

1. Allinger, N. L.; Chen, K. (1996): Hyperconjugative effects on carbon-carbon bond lengths in molecular mechanics (MM4). Journal of Computational Chemistry, vol. 17, pp. 747-755. (Pubitemid 126567076)
2. Arroyo, M.; Belytschko, T. (2002): An atomistic-based finite deformation membrane for single layer crystalline films. Journal of the Mechanics and Physics of Solids, vol. 50, no. 9, pp. 1941-1977.
3. Bloch, F. (1928): Über die Quantenmechanik der Elektronen in Kristallgittern. Zeitschrift für Physik, vol. 52, pp. 555-600.
4. Born, M.; Huang, K. (1954): Dynamical theory of crystal lattices. Oxford University Press, Oxford.
5. Brenner, D. W. (1990): Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Physical Review B, vol. 42, no. 15, pp. 9458-9471.
6. Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M. (1983): CHARMM: A program for macromolecular energy, minimization, and dynamics calculations. Journal of Computational Chemistry, vol. 4, pp. 187-217.
7. Buckingham, R. A. (1938): The classical equation of state of gaseous helium, neon and argon. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 168, no. 933, pp. 264-283.
8. Car, R.; Parrinello, M. (1985): Unified approach for molecular dynamics and density functional theory. Physical Review Letters, vol. 55, no. 22, pp. 2471-2474.
9. Chakrabarty, A.; Cagin, T. (2008): Computational studies on mechanical and thermal properties of carbon nanotube based nanostructures. CMC: Computers, Materials & Continua, vol. 7, no. 3, pp. 167-189.
10. Cheng, H.-C.; Hsu, Y.-C.; Chen, W.-H. (2009): The influence of structural defect on mechanical properties and fracture behaviors of carbon nanotubes. CMC: Computers, Materials & Continua, vol. 11, no. 2, pp. 127-146.
11. Dirac, P. (1930): Note on exchange phenomena in the Thomas atom. Proceedings of the Cambridge Philosophical Society, vol. 26, pp. 376-385.
12. Ehrenfest, P. (1927): Bemerkung über die angenäherte Gültigkeit der klassischen Mechanik innerhalb der Quantenmechanik. Zeitschrift für Physik, vol. 45, pp. 455-457.
13. Ercolessi, F.; Adams, J. (1994): Interatomic potentials from first-principles calculations: The force-matching method. Europhysics Letters, vol. 26, pp. 583-588.
14. Ericksen, J. L. (1984): The cauchy and born hypotheses for crystals. In Gurtin, M. E. (Ed): Phase Transformations and Material Instabilities in Solids, pp. 61-77. Academic Press, Inc., New York.
15. Fock, V. (1930): Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Zeitschrift für Physik, vol. 61, pp. 126-148.
16. Harik, V. M. (2002): Mechanics of carbon nanotubes: applicability of the continuum-beam models. Computational Materials Science, vol. 24, pp. 328-342. (Pubitemid 34545824)
17. Hartree, D. R. (1928): The wave mechanics of an atom with a noncoulomb central field. Part I: theory and methods. Proceedings of the Cambridge Philosophical Society, vol. 24, pp. 89.
18. Hartree, D. R. (1932): A practical method for the numerical solution of differential equations. Memoirs and Proceedings of the Manchester Literary & Philosophical Society, vol. 77, pp. 91.
19. Hilber, H. M.; Hughes, T. J. R.; Taylor, R. L. (1978): Collocation, dissipation and 'overshoot' for time integration schemes in structural dynamics. Earthquake Engineering and Structural Dynamics, vol. 6, pp. 99-117.
20. Hohenberg, P.; Kohn, W. (1964): Inhomogeneous electron gas. Physical Review, vol. 136, no. 3 B, pp. 864-871.
21. Jeng, Y.-R.; Tsai, P.-C.; Huang, G.-Z.; Chang, I.-L. (2009): An investigation into the mechanical behavior of single-walled carbon nanotubes under uniax-ial tension using molecular statics and molecular dynamics simulations. CMC: Computers, Materials & Continua, vol. 11, no. 2, pp. 109-125.
22. Kohn, W.; Sham, J. (1965): Self-consistent equations including exchange and correlation effects. Physical Review, vol. 140, no. 4 A, pp. 1133-1138.
23. Lennard-Jones, J. E. (1929): The electronic structure of some diatomic molecules. Transactions of the Faraday Society, vol. 25, pp. 668-686.
24. Levine, I. N. (1991): Quantum Chemistry. Prentice-Hall, New York, 4 edition.
25. Li, C.; Chou, T.-W. (2004): Modeling of elastic buckling of carbon nanotubes by molecular structural mechanics approach. Mechanics of Materials, vol. 36, no. 11, pp. 1047-1055.
26. Marx, D.; Hutter, J. (2000): Ab initio molecular dynamics: Theory and implementation. In Grotendorst, J. (Ed): Modern Methods and Algorithms of Quantum Chemistry, pp. 301-449. John von Neumann Institute for Computing, Jülich.
27. Mayo, S. L.; Olafson, B. D.; Goddard (III), W. A. (1990): DREIDING: A generic force field for molecular simulations. Journal of Physical Chemistry, vol. 94, pp. 8897-8909.
28. Morse, P. M. (1929): Diatomic molecules according to the wave mechanics II: Vibrational levels. Physical Review, vol. 34, pp. 57-64.
29. Nasdala, L.; Ernst, G. (2005): Development of a 4-node finite element for the computation of nano-structured materials. Computational Materials Science, vol. 33, no. 4, pp. 443-458. (Pubitemid 40466978)
30. Nasdala, L.; Ernst, G.; Lengnick, M.; Rothert, H. (2005): Finite element analysis of carbon nanotubes with Stone-Wales defects. CMES: Computer Modeling in Engineering & Sciences, vol. 7, no. 3, pp. 293-304. (Pubitemid 40539416)
31. Newmark, N. M. (1959): A method of computation for structural dynamics. Journal of Engineering Mechanics Division, vol. 85, pp. 67-94.
32. Pauling, L.; Wilson Jr., E. B. (1985): Introduction to Quantum Mechanics with Applications to Chemistry. Dover, New York.
33. Rappé, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard (III), W. A.; Skiff, W. M. (1992): UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. Journal of the American Chemical Society, vol. 114, pp. 10024-10035.
34. Rochefort, A.; Avouris, P.; Lesage, F.; Salahub, D. R. (1999): Electrical and mechanical properties of distorted carbon nanotubes. Physical Review B, vol. 60, no. 19, pp. 13824-13830.
35. Roterman, I. K.; Lambert, M. H.; Gibson, K. D.; Scheraga, H. A. (1989): A comparison of the CHARMM, AMBER and ECEPP potentials for peptides. I. Conformational predictions for the tandemly repeated peptide (Asn-Ala-Asn-Pro) 9. Journal of Biomolecular Structures and Dynamics, vol. 7, pp. 391-419. (Pubitemid 20032402)
36. Schlick, T. (2002): Molecular Modeling and Simulation. Springer, New York.
37. Schrödinger, E. (1926): Quantisierung als Eigenwertproblem. Annalen der Physik, vol. 79, pp. 361-376, 489-527.
38. Shen, S.; Atluri, S. N. (2004): Computational nano-mechanics and multi-scale simulation. CMC: Computers, Materials & Continua, vol. 1, no. 1, pp. 59-90. (Pubitemid 41270270)
39. Slater, J. C.; Koster, G. F. (1954): Simplified LCAO method for the periodic potential problem. Physical Review, vol. 94, no. 6, pp. 1498-1524.
40. Slater, J. C.; Wilson, T. M.; Wood, J. H. (1969): Comparison of several exchange potentials for electrons in the Cu+ ion. Physical Review, vol. 179, no. 1, pp. 28-38.
41. Stillinger, F. H.; Weber, T. A. (1985): Computer simulation of local order in condensed phases of silicon. Physical Review B, vol. 31, no. 8, pp. 5262-5271.
42. Tersoff, J. (1988): Empirical interatomic potential for carbon, with applications to amorphous carbon. Physical Review Letters, vol. 61, no. 25, pp. 2879-2882.
43. Tserpes, K. I.; Papanikos, P. (2005): Finite element modeling of single-walled carbon nanotubes. Composites Part B: Engineering, vol. 36, pp. 468-477. (Pubitemid 40537162)
44. van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard (III), W. A. (2001): Reaxff: A reactive force field for hydrocarbons. The Journal of Physical Chemistry A, vol. 105, no. 41, pp. 9396-9409.
45. Verlet, L. (1967): Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Physical Review, vol. 159, no. 1, pp. 98.
46. Wang, X. Y.; Wang, X. (2004): Numerical simulation for bending modulus of carbon and some explanations for experiment. Composites Part B: Engineering, vol. 35, pp. 79-86.
47. Weiner, P. K.; Kollman, P. A. (1981): Description of the AMBER program for molecular mechanics. Journal of Computational Chemistry, vol. 2, pp. 287-303.
48. Xie, G. Q.; Long, S. Y. (2006): Elastic vibration behaviors oof carbon nanotubes based on micropolar mechanics. CMC: Computers, Materials & Continua, vol. 4, no. 1, pp. 11-19. (Pubitemid 44562750)
49. Xie, G. Q.; X. Han; Long, S. Y. (2007): Characteristic of waves in a multi-walled carbon nanotube. CMC: Computers, Materials & Continua, vol. 6, no. 1, pp. 1-11. (Pubitemid 47229164)