Calculus of Variations and Geometric Measure Theory
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S. Fanzon - M. Palombaro - M. Ponsiglione

A variational model for dislocations at semi-coherent interfaces

created by ponsiglio on 30 Nov 2015
modified by fanzon on 01 Mar 2019

[BibTeX]

Published Paper

Inserted: 30 nov 2015
Last Updated: 1 mar 2019

Journal: Journal of Nonlinear Science
Volume: 27
Pages: 1435
Year: 2017
Doi: 10.1007/s00332-017-9366-5

ArXiv: 1512.03795 PDF

Abstract:

We 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 that compensate the lattice misfit at the interface, and a far field elastic energy, spent to decrease the amount of needed dislocations. We prove that the former scales like the surface area of the interface, the latter like its diameter. The proposed continuum model is deduced from some rigorous derivation from 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.


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