Modifications to the Cauchy-Born rule: Applications in the deformation of single-walled carbon nanotubes

International Journal of Solids and Structures

Volumn 43, Issue 22-23, 2006, Pages 7128-7144

  Chandraseker, Karthick ^a   Mukherjee, Subrata ^a   Mukherjee, Yu Xie ^b  

^a Cornell University ^*  (United States)

^b NONE   (United States)

Author keywords

Atomistic model; Cauchy Born rule; Constitutive; Continuum; Finite deformation; Homogeneous; Kinematic; Membrane; Non uniform; Nonlinear elasticity; Variational method

Indexed keywords

ATOMIC PHYSICS; CONTINUUM MECHANICS; DEFORMATION; GRADIENT METHODS; KINEMATICS; MEMBRANES; PROBLEM SOLVING; THEOREM PROVING; VECTORS;

ATOMISTIC MODEL; CAUCHY-BORN RULE; CONSTITUTIVES; FINITE DEFORMATION; HOMOGENEOUS; NON-UNIFORM; NONLINEAR ELASTICITY; VARIATIONAL METHOD;

CARBON NANOTUBES;

EID: 33748955199     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.03.007     Document Type: Article

References (20)

1. Arroyo M., and Belytschko T. An atomistic-based finite deformation membrane for single layer crystalline films. J. Mech. Phys. Solids 50 (2002) 1941-1977
2. Brenner D.W. Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev. B 42 (1990) 9458-9471
3. Chandraseker K., and Mukherjee S. Coupling of extension and twist in single-walled carbon nanotubes. ASME J. Appl. Mech. 73 2 (2006) 315-326
4. Cousins C. Inner elasticity. J. Phys. C 11 (1978) 4867-4879
5. Dresselhaus M.S., Dresselhaus G., and Jorio A. Unusual properties and structure of carbon nanotubes. Annu. Rev. Mater. Res. 34 (2004) 247-278
6. Ericksen J.L. The Cauchy and Born Hypotheses for crystals. In: Gurtin M.E. (Ed). Phase Transformations and Material Instabilities in Solids (1984), Academic Press, New York 61-77
7. Fung Y.C., and Tong P. Classical and Computational Solid Mechanics (2001), World Scientific, Singapore
8. Gradshteyn I.S., and Ryzhik I.M. Tables of Integrals, Series, and Products. sixth ed. (2000), Academic Press, San Diego, CA pp. 1097-1098
9. Jiang H., Zhang P., Liu B., Huang Y., Geubelle P.H., Gao H., and Hwang K.C. The effect of nanotube radius on the constitutive model for carbon nanotubes. J. Comput. Mater. Sci. 28 (2003) 429-442
10. Liu B., Jiang H., Johnson H.T., and Huang Y. The influence of mechanical deformation on the electrical properties of single wall carbon nanotubes. J. Mech. Phys. Solids 52 (2004) 1-26
11. Marsden J.E., and Hughes T.J. Mathematical Foundations of Elasticity (1983), Prentice-Hall, Englewood Cliffs, NJ
12. Ogden, R.W., 1984. Non-linear Elastic Deformations. Ellis Horwood Series in Mathematics and its Applications, Chichester, UK.
13. Shenoy V., Miller R., Tadmor E., Rodney D., Phillips R., and Ortiz M. An adaptive finite element approach to atomic-scale mechanics - the quasicontinuum method. J. Mech. Phys. Solids 47 (1999) 611-642
14. Steigmann D.J., and Ogden R.W. Elastic surface-substrate interactions. Proc. R. Soc. Lond. A 455 (1999) 437-474
15. Tadmor E., Smith G., Bernstein N., and Kaxiras E. Quasicontinuum analysis of defects in solids. Philos. Mag. A 73 6 (1996) 1529-1563
16. Tadmor E.B., Smith G.S., Bernstein N., and Kaxiras E. Mixed finite element and atomistic formulation for complex crystals. Phys. Rev. B 59 (1999) 235-245
17. Tersoff J. New empirical approach for the structure and energy of covalent systems. Phys. Rev. B 37 (1988) 6991-7000
18. Yakobson B.I. Mechanical relaxation and "intramolecular plasticity" in carbon nanotubes. Appl. Phys. Lett. 72 (1998) 918-920
19. Yakobson B.I., Campbell M.P., Brabec C.J., and Bernholc J. High strain rate fracture and C-chain unraveling in carbon nanotubes. J. Comput. Mater. Sci. 8 (1997) 341-348
20. Zhang P., Huang Y., Geubelle P.H., Klein P.A., and Hwang K.C. The elastic modulus of single-wall carbon nanotubes: a continuum analysis incorporating interatomic potentials. Int. J. Solids Struct. 39 (2002) 3893-3906