An effective implicit method for discrete dislocation dynamics simulation

Dislocations exhibit complex spatiotemporal dynamics due to their long-range mutual interactions via their induced stress fields. The mathematical formulation of this system leads to stiff differential equations. Solving them numerically with explicit methods on long time scales is computationally rather demanding. Nonetheless, all the currently applied algorithms are based on different explicit methods both in 2 and 3 dimensions [1, 2]. Although implicit methods are generally more suitable for such problems, because of the long-range interactions, the computing cost can be even higher for a large number of simulated dislocations or dislocation segments.

To find an optimal intermediate solution we developed an implicit method, which decreases the simulation runtime efficiently in 2 dimensions by reducing the complexity of the mathematical system using physics principles. Our in-depth analysis showed that, while achieving better precision, the runtime decreased with several orders of magnitude. The method can also be applied in 3D systems as well. This numerical scheme is not only significantly faster than previous ones but it also makes it possible to study the precursors of avalanches and the avalanches as well in great depth [3], making it possible to understand better the behavior of dislocation systems during plastic deformation.