Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect

Julian Braun*, Thomas Hudson, Christoph Ortner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work rigorously derives a novel far-field expansion of these fields. The expansion is computable and is expressed as a sum of continuum correctors and discrete multipole terms which decay with increasing algebraic rate as the order of the expansion increases. Truncating the expansion leaves a remainder describing the defect core structure, which is localised in the sense that it decays with an algebraic rate corresponding to the order at which the truncation occurred.

Original languageEnglish
Pages (from-to)1437-1490
Number of pages54
JournalArchive for Rational Mechanics and Analysis
Volume245
Issue number3
Early online date22 Jul 2022
DOIs
Publication statusPublished - Sep 2022

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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