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From:
N. Silvestre and D. Camotim (University of Lisbon),
“Bending instabilities of carbon nanotubes”, Chapter in book that is not identified in the pdf file, January 2009, DOI: 10.1007/978-3-642-00980-8_49
ABSTRACT: This paper presents an investigation on the buckling behaviour of single-walled carbon nanotubes (NTs) under bending and unveils several aspects concerning the dependence of critical bending curvature on the NT length. The buckling results are obtained by means of non-linear shell finite element analyses using ABAQUS code. It is shown that eigenvalue analyses do not give a correct prediction of the critical curvature of NTs under bending. Conversely, incremental-iterative non-linear analyses provide a better approximation to the molecular dynamics results due to the progressive ovalization of the NT cross- section under bending. For short NTs, the limit curvature drops with the increasing length mostly due to the decreasing influence of end effects. For moderate to long tubes, the limit curvature remains practically constant and independent on the tube length. An approximate formula based on the Brazier expression is proposed to predict the limit curvature.
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