SISOM 2006, Bucharest 17-19 May ) nn (2 , ) nn 0) n ON THE BENDING AND TORSION OF CARBON NANOTUBES Petre P. TEODORESCU , Veturia CHIROIU , Ana Maria MITU 1 2 2 2 Institute of Solid Mechanics, Bucharest, email: veturiachiroiu@yahoo.com The aim of the paper is to analyze the bending and torsion of carbon nanotubes. We are focusing on the single-walled carbon nanotubes with different chirality (armchair (, , chiral , and zigzag (. ), and perfect circular cross section, subjected to bending and torsion. A continuum nonlinear theory is applied firstly to describe the carbon nanotube deformation, and then a comparirion of results with an atomistic approach and also with experimental results are made. Key words: carbon nanotubes, bending, torsion. 1. INTRODUCTION This study deals with the carbon nanotubes deformation at bending and torsion. The carbon nanotube is a quasi-one-dimensional structure discovered by Iijima [1], Iijima and Ichihashi [2]. It is one of the most promising building blocks for future development of functional nanostructures (Srivastava, Menon and Cho [3], Gao, Cagin and Goddard [4]). The single-walled carbon nanotubes can be regarded as a rolled-up graphite sheet in cylindrical form. Thess and co-workers [5] produced crystalline ropes of metallic carbon nanotubes with 100–500 single-walled carbon nanotubes bundled into a 2D triangular lattice. The nanotube is a cylindrical molecule composed of carbon atoms, with open or closed ends. The bonding in carbon nanotubes is similar, but not identical, to the graphene sheet. To identify the types of single-walled carbon nanotubes we refer to rolling up the graphene sheet. The geometric parameter associated with this process is the roll-up vector r, which is a linear combination of the lattice basis a and b, with (, a particular integer pair (Fig. 1.1) ) nm r na mb = + , (1.1) Fig. 1.2 presents a group and also, the single carbon nanotubes. For 0 m = , we have the “zigzag” form, for , the “armchair” form, and for other “chiral”. A carbon nanotube has stable closed ends when it is larger in diameter than the (5,5) and (9,0) tubes. The shapes of the ends are not unique for tubes with the same radius. n m = Advances in multi-scale computational methods for nanostructured materials are made by coupling the continuum-models with more-realistic details at quantum and atomistic scales. For details of these methods, we suggest the review by Carlsson [9], Chiroiu et al [10], Teodorescu et al [11[, Chiroiu et al [12,13], Iordache et al [14], Ştiucă et al [15]. In this paper, we apply a continuum nonlinear theory to describe the bending and torsion of carbon nanotubes. We compare the results with an atomistic approach and also with experimental results. The conclusion of this investigation is that the nonlinear theory does not describe efficiently the nanotube behavior. The applied atomistic theory is better, with results closer to the experimental results. So, a coupled atomistic-continuum theory must be applied to describe the realistic behavior of the carbon nanotubes subjected to bending and torsion.