Dynamics for Systems of Screw Dislocations

DOI10.1137/140980065zbMath1322.34059arXiv1410.6306OpenAlexW2105814348MaRDI QIDQ5253650

Timothy Blass, Giovanni Leoni, Marco Morandotti, Irene Fonseca

Publication date: 27 May 2015

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.6306

zbMATH Keywords

differential inclusionsvariational methodsdislocation dynamicsFilippov systemsrenormalized energyscrew dislocations

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Ordinary differential inclusions (34A60) Qualitative investigation and simulation of ordinary differential equation models (34C60) Molecular, statistical, and kinetic theories in solid mechanics (74A25)

Related Items (18)

Boltzmann to Landau from the gradient flow perspective ⋮ Variational modeling of dislocations in crystals in the line-tension limit ⋮ Variational evolution of dislocations in single crystals ⋮ Renormalized energy for dislocations in quasi-crystals ⋮ Homogenization of vector-valued partition problems and dislocation cell structures in the plane ⋮ Minimising movements for the motion of discrete screw dislocations along glide directions ⋮ Convergence of Interaction-Driven Evolutions of Dislocations with Wasserstein Dissipation and Slip-Plane Confinement ⋮ Dynamics of screw dislocations: A generalised minimising-movements scheme approach ⋮ Upscaling of screw dislocations with increasing tangential strain ⋮ 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 ⋮ Properties of Screw Dislocation Dynamics: Time Estimates on Boundary and Interior Collisions ⋮ Existence and rigidity of the vectorial Peierls–Nabarro model for dislocations in high dimensions ⋮ Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space ⋮ Convergence and non-convergence of many-particle evolutions with multiple signs ⋮ On the Motion of Curved Dislocations in Three Dimensions: Simplified Linearized Elasticity ⋮ Derivation of \(\mathbf{F} = \mathbf{F}^{\operatorname{e}} \mathbf{F}^{\operatorname{p}}\) as the continuum limit of crystalline slip ⋮ Dynamics of discrete screw dislocations on glide directions

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