Discrete traveling waves: Defects in crystals

The study of dislocations in cristalline solids involves phenomena taking place at different interacting scales: from the nanoscale (a few atomic spacings, the width of dislocation cores) to the macroscale, where the collective behavior of dislocation densities controls properties such as the strength of the material. We address here the main issue at the atomic scale: the understanding of the structure and mobility of isolated dislocations.

We present a discrete model for the dynamics of dislocations in cubic metals. Numerical solutions of the model in 3D suggest that dislocations can be identified with discrete nonlinear waves. In simplified 1D and 2D geometries, we are able to obtain information about the depinning thresholds (dynamic and static Peierls stress) and the speed of the defects thanks to the analysis of traveling wave solutions of the discrete models.