Singular kernels, multiscale decomposition of microstructure, and dislocation models
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Publication:717448
DOI10.1007/s00205-010-0333-7zbMath1251.74006arXiv1003.1917OpenAlexW3104941148MaRDI QIDQ717448
Adriana Garroni, Sergio Conti, Stefan Müller
Publication date: 4 October 2011
Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1003.1917
Crystalline structure (74E15) Statistical mechanics of crystals (82D25) Micromechanical theories (74A60)
Related Items (22)
Variational modeling of dislocations in crystals in the line-tension limit ⋮ Variational Modeling of Slip: From Crystal Plasticity to Geological Strata ⋮ Long range order in atomistic models for solids ⋮ Homogenization of vector-valued partition problems and dislocation cell structures in the plane ⋮ Existence and stability of a screw dislocation under anti-plane deformation ⋮ Line-tension limits for line singularities and application to the mixed-growth case ⋮ 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 ⋮ Derivation of strain-gradient plasticity from a generalized Peierls-Nabarro model ⋮ Optimal scaling in solids undergoing ductile fracture by void sheet formation ⋮ Analytic and geometric properties of dislocation singularities ⋮ The line-tension approximation as the dilute limit of linear-elastic dislocations ⋮ \(\Gamma\)-convergence analysis of systems of edge dislocations: the self energy regime ⋮ From atomistic model to the Peierls-Nabarro model with \({\gamma}\)-surface for dislocations ⋮ Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space ⋮ Modeling of dislocations and relaxation of functionals on 1-currents with discrete multiplicity ⋮ Optimal scaling laws for ductile fracture derived from strain-gradient microplasticity ⋮ Strain-Gradient Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy with Mixed Growth ⋮ Derivation of a Line-Tension Model for Dislocations from a Nonlinear Three-Dimensional Energy: The Case of Quadratic Growth ⋮ Dynamics for Systems of Screw Dislocations ⋮ Asymptotic analysis of second order nonlocal Cahn-Hilliard-type functionals ⋮ Dislocation microstructures and strain-gradient plasticity with one active slip plane
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