Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

P. van Meurs - A. Muntean - M. A. Peletier

Upscaling of dislocation walls in finite domains

created by vanmeurs on 08 Sep 2018

[BibTeX]

preprint

Inserted: 8 sep 2018

Year: 2013

ArXiv: 1308.5071 PDF

Abstract:

We wish to understand the macroscopic plastic behaviour of metals by upscaling the micro-mechanics of dislocations. We consider a highly simplified dislocation network, which allows our microscopic model to be a one dimensional particle system, in which the interactions between the particles (dislocation walls) are singular and non-local. As a first step towards treating realistic geometries, we focus on finite-size effects rather than considering an infinite domain as typically discussed in the literature. We derive effective equations for the dislocation density by means of \Gamma-convergence on the space of probability measures. Our analysis yields a classification of macroscopic models, in which the size of the domain plays a key role.

Credits | Cookie policy | HTML 5 | CSS 2.1