A novel nonlinear constitutive relation for graphene and its consequence for developing closed-form expressions for Young's modulus and critical buckling strain of single-walled carbon nanotubes

Shodja, H. M ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1007/s00707-011-0528-5
  3. Publisher: 2011
  4. Abstract:
  5. Carbon nanotubes (CNTs) are viewed as rolled graphene. Thus, an appropriate formulation describing the behavior of CNTs must contain the key information about both their initial configuration as graphene and final configuration as CNT.On this note, to date, somemodels, in particular based on the Cauchy- Born rule, for the description of CNTs behavior exist. A simplifying assumption in some of these models is that the length and perimeter of the CNT equal the corresponding dimensions of the unrolled initial configuration, thus neglecting the induced hoop and longitudinal strains. On the other hand, the present work offers a purely nonlinear continuum model suitable for the description of the large deformation of the graphene, without the need for the simplifying assumption and employment of the Cauchy-Born rule. The presented closed-form expressions for the Young's modulus and critical buckling strain of single-walled carbon nanotubes are functions of the elastic constants of the graphene, geometrical properties of the tube section, and a new material parameter that depends on the chirality angle; the new parameter is the coefficient of the introduced nonlinear term. The computed results are in good agreement with the available molecular mechanics results reported by different investigators
  6. Keywords:
  7. Born rule ; Buckling strain ; Cauchy-Born rule ; Closed-form expression ; Geometrical property ; Initial configuration ; Large deformations ; Longitudinal strain ; Material parameter ; New parameters ; Nonlinear constitutive relation ; Nonlinear continuum model ; Nonlinear terms ; Simplifying assumptions ; Young's Modulus ; Continuum mechanics ; Elastic moduli ; Elasticity ; Graphene ; Strain ; Single-walled carbon nanotubes (SWCN)
  8. Source: Acta Mechanica ; Volume 222, Issue 1-2 , 2011 , Pages 91-101 ; 00015970 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00707-011-0528-5