\(\Gamma\)-convergence analysis of systems of edge dislocations: the self energy regime

DOI10.1007/s00205-012-0546-zzbMath1366.74006OpenAlexW1976044055MaRDI QIDQ1762438

Adriana Garroni, Lucia De Luca, Marcello Ponsiglione

Publication date: 26 November 2012

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-012-0546-z

Mathematics Subject Classification ID

Energy minimization in equilibrium problems in solid mechanics (74G65) Methods involving semicontinuity and convergence; relaxation (49J45) Homogenization in equilibrium problems of solid mechanics (74Q05) Equations linearized about a deformed state (small deformations superposed on large) (74B15)

Related Items (31)

Variational modeling of dislocations in crystals in the line-tension limit ⋮ Gradient Theory for Geometrically Nonlinear Plasticity via the Homogenization of Dislocations ⋮ Strain gradient plasticity modeling of the cyclic behavior of laminate microstructures ⋮ Elasto-plastic evolution of single crystals driven by dislocation flow ⋮ A variational model for dislocations at semi-coherent interfaces ⋮ Convergence of Interaction-Driven Evolutions of Dislocations with Wasserstein Dissipation and Slip-Plane Confinement ⋮ Line-tension limits for line singularities and application to the mixed-growth case ⋮ A classical \(\mathbb{S}^2\) spin system with discrete out-of-plane anisotropy: variational analysis at surface and vortex scalings ⋮ Low energy configurations of topological singularities in two dimensions: A Γ-convergence analysis of dipoles ⋮ Plasticity as the \(\Gamma\)-limit of a two-dimensional dislocation energy: the critical regime without the assumption of well-separateness ⋮ Semidiscrete Modeling of Systems of Wedge Disclinations and Edge Dislocations via the Airy Stress Function Method ⋮ A model for dislocations in epitaxially strained elastic films ⋮ Derivation of strain-gradient plasticity from a generalized Peierls-Nabarro model ⋮ Coarse-graining of a discrete model for edge dislocations in the regular triangular lattice ⋮ Lattices with finite renormalized Coulombian interaction energy in the plane ⋮ Variational methods for the modelling of inelastic solids. Abstracts from the workshop held February 4--10, 2018 ⋮ The line-tension approximation as the dilute limit of linear-elastic dislocations ⋮ From atomistic model to the Peierls-Nabarro model with \({\gamma}\)-surface for dislocations ⋮ Many-particle limits in molecular solvation ⋮ Metastability and dynamics of discrete topological singularities in two dimensions: a \(\Gamma\)-convergence approach ⋮ On the Motion of Curved Dislocations in Three Dimensions: Simplified Linearized Elasticity ⋮ Strain-Gradient Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy with Mixed Growth ⋮ Topological singularities in periodic media: Ginzburg-Landau and core-radius approaches ⋮ Derivation of \(\mathbf{F} = \mathbf{F}^{\operatorname{e}} \mathbf{F}^{\operatorname{p}}\) as the continuum limit of crystalline slip ⋮ Derivation of Linearized Polycrystals from a Two-Dimensional System of Edge Dislocations ⋮ Fast Automated Detection of Crystal Distortion and Crystal Defects in Polycrystal Images ⋮ Derivation of a Line-Tension Model for Dislocations from a Nonlinear Three-Dimensional Energy: The Case of Quadratic Growth ⋮ The continuum limit of interacting dislocations on multiple slip systems ⋮ Dynamics for Systems of Screw Dislocations ⋮ The antiferromagnetic xy model on the triangular lattice: topological singularities ⋮ Dynamics of discrete screw dislocations on glide directions

Cites Work

• Unnamed Item
• Singular kernels, multiscale decomposition of microstructure, and dislocation models
• Vortices in the magnetic Ginzburg-Landau model
• Gradient theory for plasticity via homogenization of discrete dislocations
• Lower bounds for the energy of unit vector fields and applications
• Finite strain discrete dislocation plasticity
• The Jacobian and the Ginzburg-Landau energy
• Dislocation microstructures and the effective behavior of single crystals
• A product-estimate for Ginzburg-Landau and corollaries
• Limiting behavior of the Ginzburg-Landau functional
• Convergence of Ginzburg-Landau functionals in three-dimensional superconductivity
• A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. I: small deformations
• A variational model for dislocations in the line tension limit
• Some remarks on Korn's inequality
• Variational equivalence between Ginzburg-Landau, XY spin systems and screw dislocations energies
• Line-Tension Model for Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy
• Lower Bounds for Generalized Ginzburg--Landau Functionals
• Gamma-convergence of gradient flows with applications to Ginzburg-Landau
• Elastic Energy Stored in a Crystal Induced by Screw Dislocations: From Discrete to Continuous
• Renormalized Energy and Forces on Dislocations
• Variational convergence for functionals of Ginzburg-Landau type

This page was built for publication: \(\Gamma\)-convergence analysis of systems of edge dislocations: the self energy regime