Mathematical Model and Computational Studies of Discrete Dislocation Dynamics

This contribution deals with the numerical simulation of dislocation dynamics, which is a topic belonging to the field of solid state physics. Dislocations are modelled as line defects in crystalline lattice causing the disturbance of the regularity of the crystallographic arrangement of atoms. From the mathematical point of view, dislocations are defined as smooth closed or open planar curves, which evolve in time, and their motion is driven by the equation for the mean curvature flow stating that the normal velocity is proportional to the mean curvature and the sum of all acting force terms. In this paper, we describe the family of evolving curves by the parametric approach, and the system of PDEs arising from the mean curvature motion law is solved by semi-implicit scheme with spatial discretization based on the flowing finite volume method. Additionally, we enhance the performance and the numerical stability of the algorithm by adding a tangential term to the motion law. The presented results of numerical simulations contain the motion of a single dislocation in the PSB channel and the motion and mutual interaction of two dislocation curves in the PSB channel.