Modeling dislocations at different scales

In this article, we give an introduction to the basic theory of dislocations and some dislocation models at different length scales. Dislocations are line defects in crystals. The continuum theory of dislocations works well at the length scale of several lattice constants away from the dislocations. In the region surrounding the dislocations (core region), the crystal lattice is heavily distorted, and atomistic models are used to describe the atomic arrangement and related properties. The Peierls-Nabarro models of dislocations incorporate the atomic features into the continuum theory, therefore provide an alternative way to understand the dislocation core properties. The numerical simulation of the collective motion and interactions of dislocations, known as dislocation dynamics, is becoming a more and more important tool for the investigation of the plastic behaviors of materials. Several simulation methods for dislocation dynamics are also reviewed in this article.