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A variational model for dislocations at semi-coherent interfaces
journal contribution
posted on 2023-06-09, 06:23 authored by Silvio Fanzon, Mariapia Palombaro, Marcello PonsiglioneWe propose and analyze a simple variational model for dislocations at semi-coherent interfaces. The energy functional describes the competition between two terms: a surface energy induced by dislocations and a bulk elastic energy, spent to decrease the amount of dislocations needed to compensate the lattice misfit. We prove that, for minimizers, the former scales like the surface area of the interface, the latter like its diameter. The proposed continuum model is built on some explicit computations done in the framework of the semi-discrete theory of dislocations. Even if we deal with finite elasticity, linearized elasticity naturally emerges in our analysis since the far-field strain vanishes as the interface size increases.
History
Publication status
- Published
File Version
- Accepted version
Journal
Journal of Nonlinear ScienceISSN
0938-8974Publisher
Springer VerlagExternal DOI
Issue
5Volume
27Page range
1435-1461Department affiliated with
- Physics and Astronomy Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-06-01First Open Access (FOA) Date
2018-02-23First Compliant Deposit (FCD) Date
2017-06-01Usage metrics
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