Dislocation dynamics: from microscopic models to macroscopic crystal plasticity

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.

References in corpus (2)

• Second-Order Elliptic Integro-Differential Equations: Viscosity Solutions' Theory Revisited
• Homogenization of dislocation dynamics

Cited by in corpus (6)

• Slow motion of particle systems as a limit of a reaction-diffusion equation with half-Laplacian in dimension one
• Jump processes as Generalized Gradient Flows
• Analysis of stable screw dislocation configurations in an anti--plane lattice model
• Long-time asymptotics for evolutionary crystal dislocation models
• From atomistic model to the Peierls-Nabarro model with $\gamma$-surface for dislocations
• The Peierls-Nabarro model as a limit of a Frenkel-Kontorova model