Upscaling of dislocation walls in finite domains

DOI10.1017/S0956792514000254zbMath1327.74131arXiv1308.5071OpenAlexW2147996660MaRDI QIDQ5499657

Patrick van Meurs, Adrian Muntean, Mark Adriaan Peletier

Publication date: 30 July 2015

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.5071

zbMATH Keywords

plasticitymultiscale\(\Gamma\)-convergencediscrete-to-continuum limitstraight edge-dislocations

Mathematics Subject Classification ID

Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) (74C05) Methods involving semicontinuity and convergence; relaxation (49J45) Homogenization in equilibrium problems of solid mechanics (74Q05) Statistical mechanics of metals (82D35) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21)

Related Items (10)

Elasto-plastic evolution of single crystals driven by dislocation flow ⋮ Derivation of the 1-D Groma-Balogh equations from the Peierls-Nabarro model ⋮ Boundary-layer analysis of a pile-up of walls of edge dislocations at a lock ⋮ From the Peierls-Nabarro model to the equation of motion of the dislocation continuum ⋮ Quantitative Estimate of the Continuum Approximations of Interacting Particle Systems in One Dimension ⋮ Asymptotic analysis of boundary layers in a repulsive particle system ⋮ Modelling with measures: approximation of a mass-emitting object by a point source ⋮ Convergence and non-convergence of many-particle evolutions with multiple signs ⋮ Discrete-To-Continuum Limits of Particles with an Annihilation Rule ⋮ The continuum limit of interacting dislocations on multiple slip systems

Cites Work

• Asymptotic behaviour of a pile-up of infinite walls of edge dislocations
• A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations
• Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
• A non-singular continuum theory of dislocations
• Scale-dependent crystal plasticity framework with dislocation density and grain boundary effects
• Asymptotics of Edge Dislocation Pile-Up against a Bimetallic Interface
• $\Gamma$-Limit of a Phase-Field Model of Dislocations
• Asymptotic Analysis of a System of Algebraic Equations Arising in Dislocation Theory
• Elastic Energy Stored in a Crystal Induced by Screw Dislocations: From Discrete to Continuous

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