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In this work, a molecular mechanics model embedded in the finite element framework is applied to analyze the buckling behaviour of carbon nanotubes. Within this model a specific finite element is set up for the underlaying interatomic potential describing the behaviour of the multi particle system. The model relies on the fully nonlinear description of the interatomic potential and the atomic kinematics. Stability points of the system are located by an accompanying eigenvalue analysis and the bifurcation point is detected using a bisection algorithm. To follow the nonlinear load-deformation path in the area of postbuckling a branch switch is performed. With the help of this molecular mechanics model, the response of carbon nanotubes on different loading conditions with respect to buckling is studied.

SUMMARY This paper analyses the buckling behaviour of single‐walled and double‐walled carbon nanotubes. The total potential of the atomic structure consists of the bonded energy and the non‐bonded energy, both resulting from interatomic potentials, as well as the energy of external contributions. In particular, the influence of the in‐layer and inter‐layer non‐bonded interactions is investigated. These non‐bonded interactions are important to avoid the nanotubes from self‐intersection or penetration and govern the morphology of the buckled tubes. The simulation model is based on a molecular statics approach embedded in the finite element framework. The search for equilibrium configurations of the structure leads to a non‐linear system of equations, which is linearised and solved iteratively. Therefore, the model relies on the fully non‐linear description of the interatomic potential and the atomic kinematics. Stability points of the loaded carbon nanotubes are detected by an accompanying eigenvalue analysis in combination with a bisection algorithm. By means of branch switching, the continuation of the non‐linear load‐deformation path in the postbuckling regime is enabled. With this framework, the buckling characteristics of carbon nanotubes in consequence of different loading conditions is studied. Results of numerical simulations are given for carbon nanotubes under torsion, axial compression and bending. Copyright © 2012 John Wiley & Sons, Ltd.

In this work, an atomistic-continuum model is applied to single-walled carbon nanotubes. The constitutive behaviour is described by the interatomic Tersoff-Brenner potential. The coupling between atomistic deformation and the deformation of the continuum is done by an expanded Cauchy-Born rule. With the help of this model, the buckling behaviour of carbon nanotubes under different loading conditions is studied. Numerical simulation results are given for two different types of loading (axial compression, torsion).