This contribution investigates the potential failure modes of single-walled carbon nanotubes under homogeneous deformations. Material failure is identified by the loss of traction increment under a given displacement increment. An atomistic-based continuum model is employed in the analysis. According to finite strain stability theory, the traction on certain plane researches a stationary point if the acoustic tensor is singular. For nanotubes, the stationary load corresponds to the incipient failure of the tube because the materials will loss its carrying capacity if loaded beyond this point. The acoustic tensor of single-walled carbon nanotube is calculated with the aid of the continuum model. The critical points under different deformations are computed numerically. For uniaxial tension, the analysis yields a critical stretch that agrees with those reported in the literature. It is found that the failure mechanism in tension corresponds to bond-breaking rupture; in compression, nanotubes fail by shear; and mixed failure modes appear under simple shear.
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