The fracture of carbon nanotubes is studied by atomistic simulations. The fracture behavior is found to be almost independent of the separation energy and to depend primarily on the inflection point in the interatomic potential. The range of fracture strains compares well with experimental results, but the predicted range of fracture stresses is markedly higher than observed. Various plausible small-scale defects do not suffice to bring the failure stresses into agreement with available experimental results. As in the experiments, the fracture of carbon nanotubes is predicted to be brittle. The results show moderate dependence of fracture strength on chirality.

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A unified stability analysis of meshless methods with Eulerian and Lagrangian kernels is presented. Three types of instabilities were identified in one dimension: an instability due to rank deficiency, a tensile instability and a material instability which is also found in continua. The stability of particle methods with Eulerian and Lagrangian kernels is markedly different: Lagrangian kernels do not exhibit the tensile instability. In both kernels, the instability due to rank deficiency can be suppressed by stress points. In two dimensions the stabilizing effect of stress points is dependent on their locations. It was found that the best approach to stable particle discretizations is to use Lagrangian kernels with stress points. The stability of the least‐squares stabilization was also studied. Copyright © 2000 John Wiley & Sons, Ltd.

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