Convergence of Interaction-Driven Evolutions of Dislocations with Wasserstein Dissipation and Slip-Plane Confinement
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Publication:4592864
DOI10.1137/16M1096098zbMath1378.49012arXiv1409.4236OpenAlexW2240307629MaRDI QIDQ4592864
Maria Giovanna Mora, Mark Adriaan Peletier, Lucia Scardia
Publication date: 9 November 2017
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1409.4236
Variational methods for problems in mechanics (70G75) Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) (74C05) Methods involving semicontinuity and convergence; relaxation (49J45) Variational principles of physics (49S05)
Related Items (20)
Variational modeling of dislocations in crystals in the line-tension limit ⋮ Variational evolution of dislocations in single crystals ⋮ Homogenization of vector-valued partition problems and dislocation cell structures in the plane ⋮ Discrete-to-continuum convergence of charged particles in 1D with annihilation ⋮ Derivation of the 1-D Groma-Balogh equations from the Peierls-Nabarro model ⋮ Energy minimisers of perturbed dislocation energies ⋮ Upscaling of screw dislocations with increasing tangential strain ⋮ Global minimizers of a large class of anisotropic attractive‐repulsive interaction energies in 2D ⋮ Discrete minimisers are close to continuum minimisers for the interaction energy ⋮ From the Peierls-Nabarro model to the equation of motion of the dislocation continuum ⋮ The equilibrium measure for an anisotropic nonlocal energy ⋮ Particle Dynamics Subject to Impenetrable Boundaries: Existence and Uniqueness of Mild Solutions ⋮ The ellipse law: Kirchhoff meets dislocations ⋮ Convergence and non-convergence of many-particle evolutions with multiple signs ⋮ Atomistic origins of continuum dislocation dynamics ⋮ Discrete-To-Continuum Limits of Particles with an Annihilation Rule ⋮ Equilibrium measure for a nonlocal dislocation energy with physical confinement ⋮ 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 of discrete screw dislocations on glide directions
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