Nonlinear elastic properties and elastic instability of single-walled carbon nanotubes (SWNTs) under large-scale axial compression were investigated by molecular simulations using the second-generation Brenner potential. It was found that the energy changes of the nanotube can be closely fitted by a cubic function of applied strains. Therefore the in-plane stiffness C of the nanotube is linearly dependent on the strain. It shows that SWNTs harden under compression but soften in tension. At large strain, C is also sensitive to chirality and diameters of nanotubes when these are small. The critical strains of compressed nanotubes are inversely proportional to their diameters on the condition that local buckling occurs in simulations, which can be properly predicted by continuum elasticity theory if the effective thickness is known.

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