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arXiv · 1308.5071

Upscaling of dislocation walls in finite domains

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

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P. van Meurs, A. Muntean, M. A. Peletier. 2013-08-23. Upscaling of dislocation walls in finite domains. https://doi.org/10.1017/s0956792514000254

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