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arXiv · 1007.2915

Homogenization of the Peierls-Nabarro model for dislocation dynamics

Régis Monneau·Stefania Patrizi
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Abstract

This paper is concerned with a result of homogenization of an integro-differential equation describing dislocation dynamics. Our model involves both an anisotropic L\'{e}vy operator of order 1 and a potential depending periodically on $u/\ep$. The limit equation is a non-local Hamilton-Jacobi equation, which is an effective plastic law for densities of dislocations moving in a single slip plane.

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Régis Monneau, Stefania Patrizi. 2010-07-17. Homogenization of the Peierls-Nabarro model for dislocation dynamics. https://arxiv.org/abs/1007.2915

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