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- Title
Expansions for the linear-elastic contribution to the self-interaction force of dislocation curves.
- Authors
VAN MEURS, PATRICK
- Abstract
The self-interaction force of dislocation curves in metals depends on the local arrangement of the atoms and on the non-local interaction between dislocation curve segments. While these non-local segment–segment interactions can be accurately described by linear elasticity when the segments are further apart than the atomic scale of size $\varepsilon$ , this model breaks down and blows up when the segments are $O(\varepsilon)$ apart. To separate the non-local interactions from the local contribution, various models depending on $\varepsilon$ have been constructed to account for the non-local term. However, there are no quantitative comparisons available between these models. This paper makes such comparisons possible by expanding the self-interaction force in these models in $\varepsilon$ beyond the O (1)-term. Our derivation of these expansions relies on asymptotic analysis. The practical use of these expansions is demonstrated by developing numerical schemes for them, and by – for the first time – bounding the corresponding discretisation error.
- Subjects
DISLOCATIONS in metals; ASYMPTOTIC expansions; ATOMIC radius; CURVES; ELASTICITY
- Publication
European Journal of Applied Mathematics, 2022, Vol 33, Issue 6, p1032
- ISSN
0956-7925
- Publication type
Article
- DOI
10.1017/S0956792521000322