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

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 rep-resents 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.

Automated summary

Continuum dislocation dynamics (CDD) describes the evolution of curved and connected dislocation lines using density-like field variables, including the volume density of loops as an additional field. The curvature field evolution equation contains numerically inconvenient higher-order derivatives of the density fields, as dislocation curvature represents a spatial derivative of the discrete dislocation density tensor. We propose a simple approximation to express curvature in terms of density fields and demonstrate its application to a benchmark problem in Mg polycrystal deformation.