Discrete homogenization in graphene sheet modeling

Journal of Elasticity

Volumn 84, Issue 1, 2006, Pages 33-68

  Caillerie, Denis ^a   Mourad, Ayman ^b,d   Raoult, Annie ^c  

^a LABORATOIRE SOLS SOLIDES STRUCTURES   (France)

^b LMC   (France)

^c Laboratoire de Modelisation et Calcul   (France)

^d UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Carbon nanotubes; Constitutive laws; Graphene sheets; Homogenization; Lattices; Molecular mechanics; Nonlinear elasticity

Indexed keywords

CARBON NANOTUBES; CRYSTALLINE MATERIALS; ELASTICITY; MOLECULAR DYNAMICS; STIFFNESS;

CONSTITUTIVE LAWS; GRAPHENE SHEETS; HOMOGENIZATION; MOLECULAR MECHANICS; NONLINEAR ELASTICITY;

AROMATIC COMPOUNDS;

EID: 33745728258     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10659-006-9053-5     Document Type: Article

References (29)

1. N.L. Allinger, Y.H. Yuh and J.H. Lii, Molecular mechanics. The MM3 force field for hydrocarbons. J. Am. Chem. Soc. 111 (1989) 8551-8566.
2. S.S. Antman, Nonlinear Problems of Elasticity. Springer, Berlin Heidelberg New York (1995).
3. A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Stuctures. North-Holland, Amsterdam (1978).
4. X. Blanc, C. Le Bris and P.-L. Lions, From molecular models to continuum mechanics. Arch. Ration. Mech. Anal. 164 (2002) 341-381.
5. A. Braides and M.S. Gelli, The passage from discrete to continuous variational problems: A nonlinear homogenization process. In: P. Ponte Castaneda (ed.), Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials. Kluwer (2004) pp. 45-63.
6. D.W. Brenner, Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev., B 42 (1990) 9458-9471.
7. D. Caillerie, A. Mourad and A. Raoult, Cell-to-muscle homogenization. Application to a constitutive law for the myocardium. M2AN Modél. Math. Anal. Numér. 37 (2003) 681-698.
8. C.F. Cornwell and L.T. Wille, Elastic properties of single-walled carbon nanotubes in compression. Solid State Commun. 101 (1997) 555-558.
9. D. Coutand, Théorèmes d'existence pour un modèle membranaire proprement invariant de plaque non linéairement élastique. C. R. Acad. Sci., Sér. 1 Paris 324 (1997) 1181-1184.
10. D. Fox, A. Raoult and J.C. Simo, A justification of nonlinear properly invariant plate theories. Arch. Ration. Mech. Anal. 124 (1993) 157-199.
11. M.E. Gurtin, An Introduction to Continuum Mechanics. Academic, New York (1981).
12. A. Krishnan, E. Dujardin, E. Ebbesen, P.N. Yianilos and M.M.J. Treacy, Young's modulus of single-walled nanotubes. Phys. Rev., B 58 (1998) 14013-14019.
13. T. Lenosky, X. Gonze, M. Teter and V. Elser, Energetics of negatively curved graphitic carbon. Nature 355 (1992) 333-335.
14. J.Z. Liu, Q. Zheng and Q. Jiang, Effect of a rippling mode on resonances of carbon nanotubes. Phys. Rev. Lett. 86 (2001) 4843-4846.
15. C.-S. Man and D.E. Carlson, On the traction problem of dead loading in linear elasticity with initial stress. Arch. Ration. Mech. Anal. 128 (1994) 223-247.
16. A. Mourad, Description topologique de l'architecture fibreuse et modélisation mécanique du myocarde. Doctoral Dissertation, Institut National Polytechnique de Grenoble, Grenoble, France (2003).
17. G. Odegard, T.S. Gates, L. Nicholson and C. Wise, Equivalent continuum modeling of nanostructured materials. NASA Technical Report, NASA TM-2001-210863 (2001).
18. D.H. Robertson, D.W. Brenner and J.W. Mintmire, Energetics of nanoscale graphitic tubules. Phys. Rev., B 45 (1992) 12592-12595.
19. E. Sanchez-Palencia, Non Homogeneous Media and Vibration Theory. Monographs in Physics, 127, Springer, Berlin Heidelberg New York (1980).
20. J. Tersoff, New empirical approach for the structure and energy of covalent systems. Phys. Rev., B 37 (1988) 6991-7000.
21. H. Tollenaere and D. Caillerie, Continuous modeling of lattice structures by homogenization. Adv. Eng. Softw. 29 (1998) 699-705.
22. M.M.J. Treacy, T.W. Ebbesen and J.M. Gibson, Exceptionally high Young's modulus observed for individual carbon nanotubes. Nature 381 (1996) 678-680.
23. Z. Tu and Z. Ou-Yang, Single-walled and multiwalled carbon nanotubes viewed as elastic tubes with the effective Young's moduli dependent on layer number. Phys. Rev., B 65 (2002) 233407-233410.
24. E.W. Wong, P.E. Sheehan and C.M. Lieber, Nanobeam mechanics: Elasticity, strength, and toughness of nanorods and nanotubes. Science 277 (1997) 1971-1975.
25. B.I. Yakobson, C.J. Brabec and J. Bernholc, Nanomechanics of carbon tubes: Instabilities beyond linear response. Phys. Rev. Lett. 76 (1996) 2511-2514.
26. M.F. Yu, B.S. Files, S. Arepalli and R.S. Ruoff, Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties. Phys. Rev. Lett. 84 (2000) 5552-5555.
27. M.F. Yu, O. Lourie, M.J. Dyer, K. Moloni, T.F. Kelly and R.S. Ruoff, Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load. Science 287 (2000) 637-640.
28. X. Zhou, J. Zhou and Z. Ou-Yang, Strain energy and Young's modulus of single-wall carbon nanotubes calculated from electronic energy-band theory. Phys. Rev., B 62 (2000) 13692-13696.
29. G. Zhou, W. Duan and B. Gu, First-principles study on morphology and mechanical properties of single-walled carbon nanotube. Chem. Phys. Lett. 333 (2001) 344-349.