Line-tension limits for line singularities and application to the mixed-growth case

DOI10.1007/s00526-023-02552-0arXiv2207.01526OpenAlexW4386784551MaRDI QIDQ6077924

Adriana Garroni, Roberta Marziani, Sergio Conti

Publication date: 27 September 2023

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.01526

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Micromechanical theories (74A60) Homogenization in equilibrium problems of solid mechanics (74Q05) PDEs in connection with mechanics of deformable solids (35Q74)

Cites Work

• Unnamed Item
• On a mesoscopic many-body Hamiltonian describing elastic shears and dislocations
• The line-tension approximation as the dilute limit of linear-elastic dislocations
• Singular kernels, multiscale decomposition of microstructure, and dislocation models
• Metastability and dynamics of discrete topological singularities in two dimensions: a \(\Gamma\)-convergence approach
• Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity
• Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of \(\mathbf F=\mathbf F^e\mathbf F^p\)
• Vortices in the magnetic Ginzburg-Landau model
• A multi-phase transition model for dislocations with interfacial microstructure
• Gradient theory for plasticity via homogenization of discrete dislocations
• New estimates for elliptic equations and Hodge type systems
• Lower bounds for the energy of unit vector fields and applications
• Lattice incompatibility and a gradient theory of crystal plasticity
• Continuum thermodynamic models for crystal plasticity including the effects of geometrically-necessary dislocations
• \(\Gamma\)-convergence analysis of systems of edge dislocations: the self energy regime
• Vortex density models for superconductivity and superfluidity
• Dislocation microstructures and strain-gradient plasticity with one active slip plane
• Korn's second inequality and geometric rigidity with mixed growth conditions
• \(\Gamma\)-convergence analysis of a generalized \(XY\) model: fractional vortices and string defects
• Plasticity as the \(\Gamma\)-limit of a two-dimensional dislocation energy: the critical regime without the assumption of well-separateness
• A variational model for dislocations in the line tension limit
• Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result
• 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
• Gradient Theory for Geometrically Nonlinear Plasticity via the Homogenization of Dislocations
• Lower Bounds for Generalized Ginzburg--Landau Functionals
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• Derivation of a Line-Tension Model for Dislocations from a Nonlinear Three-Dimensional Energy: The Case of Quadratic Growth
• Strain-Gradient Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy with Mixed Growth
• Derivation of Linearized Polycrystals from a Two-Dimensional System of Edge Dislocations
• Analysis of Stable Screw Dislocation Configurations in an Antiplane Lattice Model
• Elastic Energy Stored in a Crystal Induced by Screw Dislocations: From Discrete to Continuous
• Lower semicontinuity and existence of minimizers in incremental finite‐strain elastoplasticity
• Renormalized Energy and Forces on Dislocations
• Variational convergence for functionals of Ginzburg-Landau type
• On the characterization of geometrically necessary dislocations in finite plasticity
• Derivation of strain-gradient plasticity from a generalized Peierls-Nabarro model

This page was built for publication: Line-tension limits for line singularities and application to the mixed-growth case