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arXiv · 1411.0870

Upscaling of the dynamics of dislocation walls

Patrick van Meurs·Adrian Muntean
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Abstract

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 $Γ$-convergence of the respective energies are properties of paramount importance for our arguments.

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Patrick van Meurs, Adrian Muntean. 2014-11-04. Upscaling of the dynamics of dislocation walls. https://arxiv.org/abs/1411.0870

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