In the parametric dislocation dynamics, closed dislocation loops were described as an assembly of segments, each represented by a parametric space curve. Their equations of motion were derived from an energy variational principle, thus allowing large-scale computer simulations of plastic deformation. An investigation was made here of the limits of temporal and spatial resolution of strong dislocation interactions. The method was demonstrated to be highly accurate, with unconditional spatial convergence that was limited to distances of the order of interatomic dimensions. It was shown that stability of dislocation line shape evolution requires very short time steps for explicit integration schemes, or could be unconditionally stable for implicit time integration schemes. Limitations of the method in resolving strong dislocation interactions were established for the following mechanisms: dislocation generation, annihilation, dipole and junction formation, pile-up evolution.

Accuracy and Convergence of Parametric Dislocation Dynamics. J.Huang, N.M.Ghoniem: Modelling and Simulation in Materials Science and Technology, 2003, 11[1], 21-39