Homogenization of dislocation dynamics

TL;DR

This paper rigorously derives effective macroscopic flow rules for dislocation dynamics in materials with periodic obstacles, covering both straight and curved dislocations, to better understand plastic deformation.

Contribution

It provides a rigorous homogenization framework for dislocation dynamics, including both straight and curved dislocations, in periodic obstacle environments.

Findings

Derived effective macroscopic flow rules for dislocation motion.

Established homogenization results for both straight and curved dislocations.

Predicted elasto-visco-plastic behavior from microscopic dynamics.

Abstract

In this paper we consider the dynamics of dislocations with the same Burgers vector, contained in the same glide plane, and moving in a material with periodic obstacles. We study two cases: i) the particular case of parallel straight dislocations and ii) the general case of curved dislocations. In each case, we perform rigorously the homogenization of the dynamics and predict the corresponding effective macroscopic elasto-visco-plastic flow rule.