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Derivation of the Young’s and shear moduli of single-walled carbon nanotubes through a computational homogenization approach

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2011
auteur(s) El Khoury Elie; Messager Tanguy; Cartraud Patrice
journal (abréviation) International Journal for Multiscale Computational Engineering (Int J for Multiscale Computational Engineering)
volume (numéro) 9 (1)
pages 97 – 118
résumé In this study, the computation of the traction-torsion-bending behavior of single-walled carbon nanotubes (SWCNTs) is investigated. A structural mechanics model is used to describe the response of the nanotube, the atomic interactions being represented with 3D beams. Nanotubes are slender structures, and taking benefit from their axial periodicity or helical symmetry, homogenization theory is used to obtain their overall beam behavior from the solution of basic cell problems. These problems are solved through a finite element approach, and involve concise models, whatever the SWCNT type. The computed results show that the bending behavior appears to be decoupled of the axial one and independent of the moment direction. Young’s and shear moduli are derived, and it is shown that the Young’s moduli in traction and bending are very close. Comparisons with data of the literature reveal good agreements. At last, scale-effects are studied, and the moduli of the SWCNTs are compared to those of the graphene, thus demonstrating mechanical sensitivity to curvature.
mots clés SWCNTs ; homogenization ; helical symmetry; periodic structures; Young’s modulus ; shear modulus.
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