Numerical Simulation of Dislocation Dynamics – the Stress Field Evaluation Threshold

Abstract. The aim of this contribution is to present the current state of our research in the field of numerical simulation of dislocation motion in crystalline materials. The simulation is based on recent theory treating dislocation curves and dipolar loops interacting by means of forces of elastic nature and hindered by the lattice friction. The motion and interaction of a single parametrically described dislocation curve and one or more dipolar loops placed in 3D space is considered. The complexity of the stress fields of dipolar loops as well as of the dislocation curve necessitates application of advanced numerical algorithms to successfully solve the problem. The present numerical algorithm is based on analytical formulae for stress tensor of interaction between dislocation curve and dipolar loop, analytical interaction formulae for dipolar-to-dipolar loop interaction, parametric description of the dislocation curve (i.e. 1D description of a fully 3D problem), and the flowing finite volume method. It is showing up, that despite of using analytical formulae in the numerical algorithm, it is necessary to introduce other optimizations as distance thresholds for evaluation of these formulae.