Microstructural Comparison of the Kinematics of Discrete and Continuum Dislocations Models

TL;DR

This paper compares continuum and discrete dislocation models, developing a numerical tool for direct microstructural comparison, revealing that continuum models retain many important microstructural details.

Contribution

It introduces a numerical method to convert discrete dislocation data into continuum representations for direct comparison, highlighting microstructural similarities.

Findings

Continuum models capture key microstructural features.

The numerical tool enables direct comparison of DDD and CDD.

Continuum dislocation dynamics retain important microstructural details.

Abstract

The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation Dynamics (DDD) method are compared based on concise mathematical formulations of the coarse graining of discrete data. A numerical tool for converting from a discrete to a continuum representation of a given dislocation configuration is developed, which allows to directly compare both simulation approaches based on continuum quantities (e.g. scalar density, geometrically necessary densities, mean curvature). Investigating the evolution of selected dislocation configurations within analytically given velocity fields for both DDD and CDD reveals that CDD contains a surprising number of important microstructural details.