A mesoscale approach for dislocation density motion using a Runge‐Kutta discontinuous Galerkin method. Issue 1 (25th October 2016)

• Record Type: Journal Article
• Authors: Schulz, Katrin; Wagner, Lydia; Wieners, Christian
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 16:Issue 1(2016)
• Page Start: 403
• Page End: 404
• Publication Date: 2016-10-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201610190
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: In this note, the issue of numerical diffusion in the context of a dislocation based continuum formulation is addressed. Using a geometrical description of dislocation lines and their averages based on a higher order configuration space, a kinematic continuum model is presented for the evolution of curved dislocation lines. In order to include the physical interactions occuring between dislocation lines, an accurate numerical description of the dislocations represented by different quantities of dislocation density has to be ensured. By applying a finite volume scheme as well as a discontinuous Galerkin scheme to a simple benchmark problem, we compare the two numerical methods and discuss the results in the context of dislocation based plasticity. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)