Error-controlled switching between discrete and continuum dislocations in a unified defect framework
Abstract
Simulating defects of every dimension together is expensive, and the savings of adaptive methods are rarely tested at equal accuracy. We present a variational framework in which fields, dislocation lines and defect densities share one free energy, one dissipation law and exact ledgers of mass and Burgers vector, so that a region can change its representation without gaining or losing defects. On this basis, an allocator switches the dislocations themselves between discrete particles, where they are sparse, and a continuous density, where they are dense. The switch is made block by block from local counts, conserves the Burgers vector exactly and is controlled by a single threshold. For 5×105 dislocations, the allocator reproduces the discrete model to within 1% in the sparse region at 14-37 times lower cost, depending on the machine; the advantage grows to 81 times at 106 dislocations, and a threshold calibrated on one ensemble meets its error target on an independent one. For an idealized array of dislocation walls in copper, the allocator is 37.5 times cheaper than particle dislocation dynamics and, at almost the same cost, six times more accurate than continuum dislocation dynamics between the walls. In a three-dimensional copper model coupling grain-boundary cavitation with damage, ligaments left at nominal coalescence delay creep rupture by 25-48% (post hoc sweep). By contrast, grids refined at interfaces gain less than twofold once the active region exceeds about 30% of the domain, so representation switching, rather than grid refinement, is the effective form of adaptivity for defect-rich microstructures.
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BibTeX
@misc{linda2026errorcontrolled,
title = {{Error-controlled switching between discrete and continuum dislocations in a unified defect framework}},
author = {Albert Linda},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19841},
eprint = {2610.19841},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19841},
}
RIS
TY - UNPB
TI - Error-controlled switching between discrete and continuum dislocations in a unified defect framework
AU - Albert Linda
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19841
UR - https://arxiv.org/abs/2610.19841
AB - Simulating defects of every dimension together is expensive, and the savings of adaptive methods are rarely tested at equal accuracy. We present a variational framework in which fields, dislocation lines and defect densities share one free energy, one dissipation law and exact ledgers of mass and Burgers vector, so that a region can change its representation without gaining or losing defects. On this basis, an allocator switches the dislocations themselves between discrete particles, where they are sparse, and a continuous density, where they are dense. The switch is made block by block from local counts, conserves the Burgers vector exactly and is controlled by a single threshold. For 5×10^5 dislocations, the allocator reproduces the discrete model to within 1% in the sparse region at 14-37 times lower cost, depending on the machine; the advantage grows to 81 times at 10^6 dislocations, and a threshold calibrated on one ensemble meets its error target on an independent one. For an idealized array of dislocation walls in copper, the allocator is 37.5 times cheaper than particle dislocation dynamics and, at almost the same cost, six times more accurate than continuum dislocation dynamics between the walls. In a three-dimensional copper model coupling grain-boundary cavitation with damage, ligaments left at nominal coalescence delay creep rupture by 25-48% (post hoc sweep). By contrast, grids refined at interfaces gain less than twofold once the active region exceeds about 30% of the domain, so representation switching, rather than grid refinement, is the effective form of adaptivity for defect-rich microstructures.
ER -