Dislocation dynamics: from microscopic models to macroscopic crystal plasticity

TL;DR

This paper explores the hierarchical connection between four dislocation models, from atomic to macroscopic scales, demonstrating how each model derives from the more detailed one below.

Contribution

It establishes a systematic derivation pathway linking atomic-level models to continuum dislocation density models.

Findings

Unified framework for dislocation modeling across scales

Derivation of macroscopic models from microscopic descriptions

Enhanced understanding of dislocation behavior across different resolutions

Abstract

In this paper we study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model, the discrete dislocation dynamics and a macroscopic model with dislocation densities. We show how each model can be deduced from the previous one at a smaller scale.