Derivation of Orowan's Law from the Peierls–Nabarro Model

DOI10.1080/03605302.2012.683504zbMath1255.35215arXiv1207.4412OpenAlexW1979144568MaRDI QIDQ4902753

Stefania Patrizi, Régis Monneau

Publication date: 17 January 2013

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4412

zbMATH Keywords

transition layerperiodic homogenizationdislocation dynamicsnon-local equationsPeierls-Nabarro modelOrowan's law

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Stress concentrations, singularities in solid mechanics (74G70) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27) PDEs in connection with mechanics of deformable solids (35Q74) Integro-partial differential equations (35R09)

Related Items (10)

A fractional glance to the theory of edge dislocations ⋮ Discrete-to-continuum convergence of charged particles in 1D with annihilation ⋮ Derivation of the 1-D Groma-Balogh equations from the Peierls-Nabarro model ⋮ Discrete Dislocation Dynamics with Annihilation as the Limit of the Peierls–Nabarro Model in One Dimension ⋮ From the Peierls-Nabarro model to the equation of motion of the dislocation continuum ⋮ Homogenization of the Peierls-Nabarro model for dislocation dynamics ⋮ Threshold phenomenon for homogenized fronts in random elastic media ⋮ From atomistic model to the Peierls-Nabarro model with \({\gamma}\)-surface for dislocations ⋮ Discrete-To-Continuum Limits of Particles with an Annihilation Rule ⋮ Homogenization and Orowan's law for anisotropic fractional operators of any order

Cites Work

• Nonlinear diffusion of dislocation density and self-similar solutions
• Homogenization of fully overdamped Frenkel-Kontorova models
• Motion by curvature by scaling nonlocal evolution equations
• Fractal first-order partial differential equations
• Stability of a dislocation : Discrete model
• Layer solutions in a half‐space for boundary reactions
• Unnamed Item

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