Derivation and study of dynamical models of dislocation densities

TL;DR

This paper derives mean field transport models for dislocation densities from microscopic dislocation dynamics, coupling them with elasticity equations, and provides rigorous existence results for some models.

Contribution

It introduces a formal derivation of dislocation density models from microscopic dynamics and proves existence of solutions for these models.

Findings

Derivation of mean field transport equations for dislocation densities

Coupling of dislocation models with elasticity equations

Existence proofs for solutions of the derived models

Abstract

In this paper, starting from the microscopic dynamics of isolated dislocations, we explain how to derive formally mean field models for the dynamics of dislocation densities. Essentially these models are tranport equations, coupled with the equations of elasticity. Rigorous results of existence of solutions are presented for some of these models and the main ideas of the proofs are given.