Variational modeling of dislocations in crystals in the line-tension limit
type: Item
instance of: scholarly article
title: Variational modeling of dislocations in crystals in the line-tension limit
zbMATH Open document ID: 1402.82018
DOI: 10.4171/176-1/27
author: Pilar Ariza
author: Sergio Conti
author: Adriana Garroni
author: M. Ortiz
publication date: 2018-11-14T00:00:00Z
review text: Summary: Dislocations are line singularities in crystals which are crucial for the plastic deformation of materials. Mathematically they can be modeled as measures supported on rectifiable curves, or as vector-valued one-currents. They have a lattice-valued multiplicity, which is a conserved quantity, in the sense that the divergence of the measure (or the boundary of the current) vanishes. Dislocations are necessarily accompanied by large elastic strains, and indeed their energetics can be understood starting from the theory of elasticity, in an appropriate scaling regime. We discuss recent progress in the rigorous derivation of dislocation models in the line-tension regime from linear elasticity, and their application to specific problems in metals. We present numerical simulations on dislocations in bcc molybdenum which show how our line-tension model provides a simple and efficient description of dislocation structures. For the entire collection see [Zbl 1396.00017].
Mathematics Subject Classification ID: 82D25
Mathematics Subject Classification ID: 74N05
zbMATH DE Number: 6979404
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/176-1/27
OpenAlex ID: W4244140488
cites work: Variational convergence for functionals of Ginzburg-Landau type
cites work: Metastability and dynamics of discrete topological singularities in two dimensions: a \(\Gamma\)-convergence approach
cites work: Functionals defined on partitions in sets of finite perimeter. I: Integral representation and Gamma-convergence
cites work: Functionals defined on partitions in sets of finite perimeter. II: Semicontinuity, relaxation and homogenization
cites work: Discrete crystal elasticity and discrete dislocations in crystals
cites work: Vortex density models for superconductivity and superfluidity
cites work: Dynamics for Systems of Screw Dislocations
cites work: Density of polyhedral partitions
cites work: A multi-phase transition model for dislocations with interfacial microstructure
cites work: Renormalized Energy and Forces on Dislocations
cites work: Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity
cites work: Singular kernels, multiscale decomposition of microstructure, and dislocation models
cites work: Dislocation microstructures and strain-gradient plasticity with one active slip plane
cites work: Homogenization of vector-valued partition problems and dislocation cell structures in the plane
cites work: The line-tension approximation as the dilute limit of linear-elastic dislocations
cites work: \(\Gamma\)-convergence analysis of systems of edge dislocations: the self energy regime
cites work: Q5565773
cites work: Homogenization of fully overdamped Frenkel-Kontorova models
cites work: Gradient theory for plasticity via homogenization of discrete dislocations
cites work: $\Gamma$-Limit of a Phase-Field Model of Dislocations
cites work: A variational model for dislocations in the line tension limit
cites work: Asymptotic behaviour of a pile-up of infinite walls of edge dislocations
cites work: Q2965997
cites work: Local minimizers of the Ginzburg-Landau energy with magnetic field in three dimensions
cites work: Local minimizers with vortex filaments for a Gross-Pitaevsky functional
cites work: A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals.
cites work: Equation of State Calculations by Fast Computing Machines
cites work: Homogenization of the Peierls-Nabarro model for dislocation dynamics
cites work: Convergence of Interaction-Driven Evolutions of Dislocations with Wasserstein Dissipation and Slip-Plane Confinement
cites work: Geometric rigidity for incompatible fields and an application to strain-gradient plasticity
cites work: Q3827224
cites work: Elastic Energy Stored in a Crystal Induced by Screw Dislocations: From Discrete to Continuous
cites work: Currents and dislocations at the continuum scale
cites work: Line-Tension Model for Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy
description: scientific article; zbMATH DE number 6979404