A variational model for dislocations at semi-coherent interfaces

Fanzon, Silvio, Palombaro, Mariapia and Ponsiglione, Marcello (2017) A variational model for dislocations at semi-coherent interfaces. Journal of Nonlinear Science. ISSN 0938-8974

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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 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Research Centres and Groups: Analysis and Partial Differential Equations Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 01 Jun 2017 10:19
Last Modified: 01 Jun 2017 10:25
URI: http://sro.sussex.ac.uk/id/eprint/68217

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