A computationally efficient implementation of continuum dislocation dynamics: Formulation and application to ultrafine-grained Mg polycrystals

TL;DR

This paper introduces a simplified, computationally efficient method for continuum dislocation dynamics that approximates curvature to reduce numerical complexity, demonstrated through deformation modeling of Mg polycrystals.

Contribution

It proposes an approximation to express dislocation curvature in terms of density fields, simplifying the evolution equations in continuum dislocation dynamics.

Findings

The approximation reduces computational complexity.

Application to Mg polycrystals shows accurate deformation modeling.

Method maintains essential physical features of dislocation evolution.

Abstract

Continuum dislocation dynamics (CDD) represents the evolution of systems of curved and connected dislocation lines in terms of density-like field variables which include the volume density of loops (or 'curvature density') as an additional field. Since dislocation curvature represents a spatial derivative of the underlying discrete dislocation density tensor, the curvature field evolution equation of necessity contains numerically inconvenient higher-order derivatives of the density fields. We propose a simple approximation to express curvature in terms of density fields, and demonstrate its application to a benchmark problem in deformation of Mg polycrystals.