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Dislocation dynamics: from microscopic models to macroscopic crystal plasticity

El Hajj, Ahmad; Ibrahim, Hassan; Monneau, Régis (2009), Dislocation dynamics: from microscopic models to macroscopic crystal plasticity, Continuum Mechanics and Thermodynamics, 21, 2, p. 109-123. http://dx.doi.org/10.1007/s00161-009-0103-7

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00349568/en/
Date
2009
Journal name
Continuum Mechanics and Thermodynamics
Volume
21
Number
2
Publisher
Springer
Pages
109-123
Publication identifier
Metadata
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Author(s)
El Hajj, Ahmad
Ibrahim, Hassan
Monneau, Régis
Abstract (EN)
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.
Subjects / Keywords
Non local equations; Hamilton-Jacobi equations; Periodic homogenization; Phase field model; Frenkel-Kontorova model; Discrete to continuum approach