Atomistic simulations of nanotube fracture and stability analysis of particle methods

The fracture of carbon nanotubes is studied by molecular mechanics 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 fracture strain of a zigzag nanotube is predicted to be between 10% and 15%, which compares reasonably well with experimental results. The predicted range of fracture stresses is 65GPa to 93 GPa and is markedly higher than observed. Including the above values, the failure stresses and strains of nanotubes given by theoretical or numerical predictions are much higher than observed in experiments. We show that defects can explain part of this discrepancy: for an n-atom defect with 2 ≤ n ≤ 8, the range of failure stresses for a molecular mechanics calculation is found to be 36GPa to 64 GPa. This compares quite well with the larger experimental failure stresses; the range of experimental values is 11GPa to 63 GPa. The computed failure strains are 4% to 8%, whereas the experimental values are 2% to 13%. The underprediction of failure strains can be explained by the slippage that may have occurred in the experiments. The failure processes of nanotubes are clearly brittle in both the experiments and our calculations.; A coupling methods for continuum models with molecular models are developed. Two methods are studied here: the overlapping domain decomposition method and the edge-to-edge decomposition method. These two methods enforce the compatibility on the overlapping domain or interface nodes/atoms by the Lagrange multiplier method or the augmented Lagrangian method. These coupling methods can also be applied to coupling finite element methods with particle methods.; A stability analysis of particle methods with corrected derivatives is made for both Eulerian and Lagrangian kernels. Both nodal integration and stress points are analyzed. Two types of instabilities arise due to the discretization: an instability due to rank deficiency and a tensile instability. It is shown that Lagrangian kernels do not exhibit the tensile instability and the instability due to rank deficiency can be suppressed by stress points with suitable locations. The effects of particle discretizations on the reproducibility of the onset of material instabilities are analyzed in two dimensions. It is shown that Eulerian kernels severely distort the domain of material stability, so that material instabilities occur in tension (these are similar to tensile instabilities). On the other hand, for Lagrangian kernels, the domain of material stability is reproduced very well. The combination of stress points and Lagrangian kernels results in a stable method.