Calculus of Variations and Geometric Measure Theory

P. van Meurs - A. Muntean

Upscaling of the dynamics of dislocation walls

created by vanmeurs on 08 Sep 2018



Inserted: 8 sep 2018

Year: 2014

ArXiv: 1411.0870 PDF


We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in GPPS13. The proof of the upscaling procedure (i.e. the discrete-to-continuum passage) relies on the gradient flow structure of both the discrete and continuous energies of dislocations set in a suitable evolutionary variational inequality framework. Moreover, the convexity and $\Gamma$-convergence of the respective energies are properties of paramount importance for our arguments.