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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 108
Edited by: J. Kruis, Y. Tsompanakis and B.H.V. Topping
Paper 240

On the Continuum Modelling of Carbon Nano Tubes

H. Aminpour and N. Rizzi

Università degli Studi Roma Tre, Rome, Italy

Full Bibliographic Reference for this paper
H. Aminpour, N. Rizzi, "On the Continuum Modelling of Carbon Nano Tubes", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 240, 2015. doi:10.4203/ccp.108.240
Keywords: nonlinear elasticity, bifurcation analysis, microstructured continua, single walled carbon nano sheets.

A one-dimensional continuum endowed with internal structure, previously introduced by the authors, is extended and generalized by giving a procedure for constructing the constitutive functions. Starting from the reference configuration of a carbon nano sheet (CNS), a representative elementary volume (REV) is chosen. The deformation measures of the REV are identified with the change of the length of the carbon-carbon (C-C) bonds and angle variation between each pair of adjacent bonds. The strain energy density of the REV is given as a standard function of the microscopic strain measures. A relationship between the micro and the continuum strain measures is then established, this leading to an expression of the strain energy density of the REV in terms of the latter strains. Making the derivative of this energy with respect to its arguments the constitutive functions for the one-dimensional continuum are derived. The geometric and mechanical properties of a graphene nano sheet are used to construct its equivalent continuum and some numerical comparisons discussed. Although the procedure is established for a CNS, its extension to carbon nano tubes (CNTs) involves only simple geometric computations.

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