Existence and stability of a screw dislocation under anti-plane deformation

Abstract

We formulate a variational model for a geometrically necessary screw dislocation in an anti-plane lattice model at zero temperature. Invariance of the energy functional under lattice symmetries renders the problem non-coercive. Nevertheless, by establishing coercivity with respect to the elastic strain and a concentration compactness principle, we prove existence of a global energy minimiser and thus demonstrate that dislocations are globally stable equilibria within our model.

33 Pages, 7 Figures

References in corpus (2)

• An Exactly Solvable Phase-Field Theory of Dislocation Dynamics, Strain Hardening and Hysteresis in Ductile Single Crystals
• Singular kernels, multiscale decomposition of microstructure, and dislocation models

Cited by in corpus (6)

• Analysis of stable screw dislocation configurations in an anti--plane lattice model
• Many-particle limits and non-convergence of dislocation wall pile-ups
• Upscaling a model for the thermally-driven motion of screw dislocations
• From atomistic model to the Peierls-Nabarro model with $\gamma$-surface for dislocations
• Atomistic modelling of near-crack-tip plasticity
• A Novel Discrete Theory of a Screw Dislocation in the BCC Crystal Lattice