Materials Science and Engineering A 454–455 (2007) 170–177 A molecular-mechanics based finite element model for strength prediction of single wall carbon nanotubes M. Meo ∗ , M. Rossi Material Research Center, Department of Mechanical Engineering, University of Bath, Bath, Ba2 7AY, UK Received 1 August 2005; accepted 1 November 2006 Abstract The aim of this work was to develop a finite element model based on molecular mechanics to predict the ultimate strength and strain of single wallet carbon nanotubes (SWCNT). The interactions between atoms was modelled by combining the use of non-linear elastic and torsional elastic spring. In particular, with this approach, it was tried to combine the molecular mechanics approach with finite element method without providing any not-physical data on the interactions between the carbon atoms, i.e. the CC-bond inertia moment or Young’s modulus definition. Mechanical properties as Young’s modulus, ultimate strength and strain for several CNTs were calculated. Further, a stress–strain curve for large deformation (up to 70%) is reported for a nanotube Zig-Zag (9,0). The results showed that good agreement with the experimental and numerical results of several authors was obtained. A comparison of the mechanical properties of nanotubes with same diameter and different chirality was carried out. Finally, the influence of the presence of defects on the strength and strain of a SWNT was also evaluated. In particular, the stress–strain curve a nanotube with one-vacancy defect was evaluated and compared with the curve of a pristine one, showing a reduction of the ultimate strength and strain for the defected nanotube. The FE model proposed demonstrate to be a reliable tool to simulate mechanical behaviour of carbon nanotubes both in the linear elastic field and the non-linear elastic field. © 2007 Published by Elsevier B.V. Keywords: Carbon nanotubes; Molecular mechanics; Young’s modulus; Mechanical properties; Finite element analysis 1. Introduction Since their discovery carbon nanotubes [1] have attracted considerable attention in scientific communities. This is partly due to their remarkable mechanical, electrical and thermal properties. In particular, material composites such as carbon nan- otube, nanoparticle-reinforced polymers and metals have shown potentially wide application. Specifically to mechanical properties, single wall nanotubes (SWNTs) have the highest Young’s modulus about 1TPa, if normalized to their diameter, and this is one of the main reason why carbon nanotubes (CNTs) have attracted much interest for low weight structural composites [2]. A detailed summary of CNTs mechanical properties can be found in [3]. A Young’s modulus for SWNTs and multi wall nan- otubes (MWNTs) was reported to be 1.25 TPa, while a Poisson ∗ Corresponding author. Tel.: +44 1234 750111x5220; fax: +44 1234 752149. E-mail address: m.meo@bath.ac.uk (M. Meo). ratio around 0.14–0.28 was reported depending on the approach and the energy potential used. Further, experimental data of 15 SWNT bundles under tensile load showed that, the Young’s modulus ranged from 0.32 up to 1.47 TPa with an average of 1.02 TPa. The tensile strength ranged from 13 to 53 GPa [4]. In the case of MWNTs a Young’s modulus of 0.9 TPa was estimated by conducting pulling and bending tests [5]. Computational simulation for predicting mechanical prop- erties of CNTs has been recognised to be a powerful tool to overcome the difficulties arising from the measurements of nanoscale dimensions. Several approaches can be used to eval- uate the mechanical properties of SWNT and MWNT [6]. Xiao et al. [8] found a tensile strength for Armchair (126.2 GPa) and Zig-Zag (94.5 GPa) with a maximum strain of 23.1% and 15.6–17.5%, respectively. Natsuki and Endo [12], predicted the maximum stress to be around 70 GPa at 11% of strain for the Zig- Zag nanotube and 88 GPa at 15% for Armchair. Sun [13] found a tensile strength from 77 GPa (Zig-Zag) up to 101 GPa (Arm- chair). Further, an independence of the tensile strength from nanotube diameter was found. 0921-5093/$ – see front matter © 2007 Published by Elsevier B.V. doi:10.1016/j.msea.2006.11.158