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| HAL: hal-00504598, version 1 |
| arXiv: 1007.2915 |
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| Homogenization of the Peierls-Nabarro model for dislocation dynamics and the Orowan's law |
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| Régis Monneau 1, 2Stefania Patrizi |
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| (2010-07-17) |
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| 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. In dimension 1, we are able to characterize the Hamiltonian of the limit equation close to the origin, recovering a property known in physics as the Orowan's law. |
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| 1: | Centre d'enseignement et de recherche en mécanique des sols (ENPC-CERMES) |
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LCPC – Institut Navier – Ecole des Ponts ParisTech |
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| 2: | Laboratoire Navier |
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Ecole des Ponts ParisTech – CNRS : UMR8205 – IFSTTAR |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1007.2915 |
| hal-00504598, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00504598 | |
| oai:hal.archives-ouvertes.fr:hal-00504598 | |
| From: Stefania Patrizi | |
| Submitted on: Tuesday, 20 July 2010 16:46:45 | |
| Updated on: Wednesday, 10 November 2010 13:29:44 | |
