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Dislocation dynamics: from microscopic models to macroscopic crystal plasticity |
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| Authors: | A. El Hajj H. Ibrahim R. Monneau |
| Affiliation: | (1) CERMICS, Ecole Nationale des Ponts et Chaussées 6 et 8 avenue Blaise Pascal Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France;(2) LaMA-Liban, Lebanese University, P.O. Box 826, Tripoli, Lebanon |
| Abstract: | In this paper we study the connection between four models describing dislocation dynamics: a generalized 2D Frenkel-Kontorova model at the atomic level, the Peierls-Nabarro model, the discrete dislocation dynamics and a macroscopic model with dislocation densities. We show how each model can be deduced from the previous one at a smaller scale. |
| Keywords: | Discrete to continuum approach Frenkel-Kontorova model Phase field model Particle systems Periodic homogenization Hamilton-Jacobi equations Non local equations |
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