The effect of nanotube radius on the constitutive model for carbon nanotubes

Computational Materials Science

Volumn 28, Issue 3-4 SPEC. ISS., 2003, Pages 429-442

  Jiang, H ^a   Zhang, P ^b   Liu, B ^a   Huang, Y ^a   Geubelle, P H ^c   Gao, H ^d   Hwang, K C ^e  

^a United States of America   (United States)

^b UNIVERSITY OF CONNECTICUT   (United States)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^d MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

^e TSINGHUA UNIVERSITY   (China)

Author keywords

Carbon nanotube; Constitutive model; Continuum; Nanotube radius

Indexed keywords

ATOMS; COMPUTER SIMULATION; CONTINUUM MECHANICS; TORSIONAL STRESS; TRANSMISSION ELECTRON MICROSCOPY;

CONSTITUTIVE MODELS;

CARBON NANOTUBES;

EID: 0142186003     PISSN: 09270256     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.commatsci.2003.08.004     Document Type: Conference Paper

References (49)

1. Iijima S. Helical microtubules of graphite carbon. Nature. 354:1991;56-58.
2. Treacy M.M.J., Ebbesen T.W., Gibson J.M. Exceptionally high Young's modulus observed for individual carbon nanotubes. Nature. 381:1996;678-680.
3. Krishnan A., Dujardin E., Ebbesen T.W., Yianilos P.N., Treacy M.M.J. Young's modulus of single-walled nanotubes. Physical Review B. 58:1998;14013-14019.
4. Wong E.W., Sheehan P.E., Lieber C.M. Nanobeam mechanics: Elasticity, strength, and toughness of nanorods and nanotubes. Science. 277:1997;1971-1975.
5. Salvetat J.-P., Briggs G.A.D., Bonard J.-M., Bacsa R.R., Kulik A.J. Elastic and shear moduli of single-walled carbon nanotube ropes. Physical Review Letters. 82:1999;944-947.
6. Tombler T.W., Zhou C., Alexseyev L., Kong J., Dai H., Liu L., Jayanthi C.S., Tang M., Wu S.-Y. Reversible electromechanical characteristics of carbon nanotubes under local-probe manipulation. Nature. 405:2000;769-772.
7. Yu M.-F., Files B.S., Arepalli S., Ruoff R.S. Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties. Physical Review Letters. 84:2000;5552-5555.
8. Yu M.-F., Dyer M.J., Skidmore G.D., Rohrs H.W., Lu X., Ausman K.D., von Ehr J.R., Ruoff R.S. Three-dimensional manipulation of carbon nanotubes under a scanning electron microscope. Nanotechnology. 10:1999;244-252.
9. Muster J., Burghard M., Roth S., Duesberg G.S., Hernández E., Rubio A. Scanning force microscopy characterization of individual carbon nanotubes on electrode arrays. Journal of Vacuum Science and Technology B. 16:1998;2796-2801.
10. Lourie O., Wagner H.D. Evaluation of young's modulus of carbon nanotubes by micro-raman spectroscopy. Journal of Materials Research. 13:1998;2418-2422.
11. Pan Z.W., Xie S.S., Lu L., Chang B.H., Sun L.F., Zhou W.Y., Wang G., Zhang D.L. Tensile tests of ropes of very long aligned multiwall carbon nanotubes. Applied Physics Letters. 74:1999;3152-3154.
12. Robertson D.H., Brenner D.W., Mintmire J.W. Energetics of nanoscale graphitic tubules. Physical Review B. 45:1992;12592-12595.
13. Overney G., Zhong W., Tománek D. Structural rigidity and low-frenquency vibrational modes of long carbon tubules. Zeitschrift für Physik D: Atoms, Molecules and Clusters. 27:1993;93-96.
14. Molina J.M., Savinsky S.S., Khokhriakov N.V. A tight-binding model for calculations of structures and properties of graphitic nanotubes. Journal of Chemical Physics. 104:1996;4652-4656.
15. Yakobson B.I., Brabec C.J., Bernholc J. Nanomechanics of carbon tubes: Instabilities beyond linear response. Physical Review Letters. 76:1996;2511-2514.
16. Cornwell C.F., Wille L.T. Elastic properties of single-walled carbon nanotubes in compression. Solid State Communications. 101:1997;555-558.
17. Lu J.P. Elastic properties of carbon nanotubes and nanoropes. Physical Review Letters. 79:1997;1297-1300.
18. Halicioglu T. Stress calculations for carbon nanotubes. Thin Solid Films. 312:1998;11-14.
19. z composite nanotubes. Physical Review Letters. 80:1998;4502-4505.
20. Hernández E., Goze C., Bernier P., Rubio A. Elastic properties of single-wall nanotubes. Applied Physics A. 68:1999;287-292.
21. Goze C., Vaccarini L., Henrard L., Bernier P., Hernandez E., Rubio A. Elastic and mechanical properties of carbon nanotubes. Synthetic Metals. 103:1999;2500-2501.
22. Sánchez-Portal D., Artacho E., Soler J.M., Rubio A., Ordejón P. Ab Initio structural, elastic, and vibrational properties of carbon nanotubes. Physical Review B. 59:1999;12678-12688.
23. Lier G.V., Alsenoy C.V., Doran V.V., Geerlings P. Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene. Chemical Physics Letters. 326:2000;181-185.
24. Popov V.N., van Doren V.E., Balkanski M. Elastic properties of single-walled carbon nanotubes. Physical Review B. 61:2000;3078-3084.
25. Prylutskyy Y.I., Durov S.S., Ogloblya O.V., Buzaneva E.V., Scharff P. Molecular dynamics simulations of mechanical, vibrational and electronic properties of carbon nanotubes. Computational Materials Science. 17:2000;352-355.
26. Vaccarini L., Goze C., Henrard L., Hernández E., Bernier P., Rubio A. Mechanical and electronic properties of carbon and boron-nitride nanotubes. Carbon. 38:2000;1681-1690.
27. Zhou G., Duan W., Gu B. First-principles study on morphology and mechanical properties of single-walled carbon nanotube. Chemical Physics Letters. 333:2001;344-349.
28. Tadmor E.B., Ortiz M., Philips R. Quasicontinuum analysis of defects in solids. Philosophical Magazine A. 73:1996;1529-1563.
29. Tadmor E.B., Philips R., Ortiz M. Mixed atomistic and continuum models of deformation in solids. Langmuir. 12:1996;4529-4534.
30. Tadmor E.B., Smith G.S., Bernstein N., Kaxiras E. Mixed finite element and atomistic formulation for complex crystals. Physical Review B. 59:1999;235-245.
31. Gao H., Klein P.A. Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. Journal of the Mechanics and Physics of Solids. 46:1998;187-218.
32. Klein P.A., Gao H. Crack nucleation and growth as strain localization in a virtual-bond continuum. Engineering Fracture Mechanics. 61:1998;21-48.
33. Friesecke G., James R.D. A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods. Journal of the Mechanics and Physics of Solids. 48:2000;1519-1540.
34. Arroyo M., Belytschko T. An atomistic-based finite deformation membrane for single layer crystalline films. Journal of the Mechanics and Physics of Solids. 50:2002;1941-1977.
35. Zhang P., Huang Y., Geubelle P.H., Hwang K.C. On the continuum modeling of carbon nanotubes. Acta Mechanica Sinica. 18:2002;528-536.
36. Zhang P., Huang Y., Geubelle P.H., Klein P.A., Hwang K.C. The elastic modulus of single-wall carbon nanotubes: A continuum analysis incorporating interatomic potentials. International Journal of Solids and Structures. 39:2002;3893-3906.
37. P. Zhang, H. Jiang, Y. Huang, P.H. Geubelle, K.C. Hwang, An atomistic-based continuum theory for carbon nanotubes: Analysis of fracture nucleation, Journal of the Mechanics and Physics of Solids (in press).
38. Y. Huang, Z.L. Wang, Mechanics of carbon nanotubes, in: B. Karihaloo, R. Ritchie, I. Milne (Eds.), Comprehensive Structural Integrity Handbook, in: W. Gerberwich, W. Yang (Eds.), Interfacial and Nanoscale Fracture, vol. 8, Elsevier Science, 2003, pp. 551-579, Chapter 8.16.
39. Born M., Huang K. Dynamical Theory of the Crystal Lattices. 1954;Oxford University Press, Oxford.
40. Milstein F. Review: theoretical elastic behaviour at large strains. Journal of Material Science. 15:1980;1071-1084.
41. Weiner J.H. Statistical Mechanics of Elasticity. 1983;John Wiley & Sons, New York.
42. Brenner D.W. Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Physical Review B. 42:1990;9458-9471.
43. Yakobson B.I., Campbell M.P., Brabec C.J., Bernholc J. High strain rate fracture and C-chain unraveling in carbon nanotubes. Computational Materials Science. 8:1997;341-348.
44. Zhang P., Huang Y., Gao H., Hwang K.C. Fracture nucleation in single-wall carbon nanotubes under tension: a continuum analysis incorporating interatomic potentials. Journal of Applied Mechanics. 69:2002;454-458.
45. Dresselhaus M.S., Jishi R.A., Dresselhaus G., Inomata D., Nakao K., Saito R. Group theoretical concepts for carbon nanotubes. Molecular Materials. 4:1994;27-40.
46. Sánchez-Portal D., Artacho E., Soler J.M. Ab initio structure, elastic, and vibrational properties of carbon nanotubes. Physical Review B. 59:1999;12678-12688.
47. B.I. Yakobson, P. Avouris, Mechanical properties of carbon nanotubes, in: M.S. Dresselhaus, G. Dresselhaus, P. Avouris (Eds.), Carbon Nanotubes, Vol. 80 of Topics in Applied Physics, 2001, pp. 287-329.
48. B. Liu, H. Jiang, H.T. Johnson, Y. Huang, The influence of mechanical deformation on the electrical properties of single wall-carbon nanotubes, Journal of the Mechanics and Physics of Solids (in press).
49. H. Jiang, X.Q. Feng, Y. Huang, K.C. Hwang, P.D. Wu, Defect nucleation in carbon nanotubes under tension and torsion: Stone-Wales transformation, Computer Methods in Applied Mechanics and Engineering (in press).