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For the specific citations listed in the insert see the B. Safael et al citation (below) that is listed in the huge bibliography, which is downloadable from the Bibliography page of shellbuckling.com.
This and the next image are from:
B. Safaei (1), P. Naseradinmousavi (2) and A. Rahmani (3)
(1) Young Researchers and Elite Club, Electronic Branch, Islamic Azad University, Tehran, Iran
(2) Department of Mechanical Engineering, San Diego State University (SDSU), San Diego, CA 92115, USA
(3) Department of Mechanical Engineering, Ajabshir Branch, Islamic Azad University, Ajabshir, Iran
“Development of an accurate molecular mechanics model for buckling behavior of multi-walled carbon nanotubes under axial compression”, Journal of Molecular Graphics and Modelling, Vol. 65, pp 43-60, 2016 DOI: 10.1016/j.jmgm.2016.02.001
ABSTRACT: In the present paper, an analytical solution based on a molecular mechanics model is developed to evaluate the elastic critical axial buckling strain of chiral multi-walled carbon nanotubes (MWCNTs). To this end, the total potential energy of the system is calculated with the consideration of the both bond stretching and bond angular variations. Density functional theory (DFT) in the form of generalized gradient approximation (GGA) is implemented to evaluate force constants used in the molecular mechanics model. After that, based on the principle of molecular mechanics, explicit expressions are proposed to obtain elastic surface Young’s modulus and Poisson’s ratio of the single-walled carbon nanotubes corresponding to different types of chirality. Selected numerical results are presented to indicate the influence of the type of chirality, tube diameter, and number of tube walls in detailed. An excellent agreement is found between the present numerical results and those found in the literature which confirms the validity as well as the accuracy of the present closed-form solution. It is found that the value of critical axial buckling strain exhibit significant dependency on the type of chirality and number of tube walls.
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