A Variational Model for Dislocations at Semi-coherent Interfaces

Fanzon, Silvio; Palombaro, Mariapia; Ponsiglione, Marcello

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.

Citation

Fanzon, S., Palombaro, M., & Ponsiglione, M. (2017). A Variational Model for Dislocations at Semi-coherent Interfaces. Journal of Nonlinear Science, 27(5), 1435-1461. https://doi.org/10.1007/s00332-017-9366-5

• Journal Article Type: Article
• Acceptance Date: Jan 28, 2017
• Online Publication Date: Feb 22, 2017
• Publication Date: Oct 1, 2017
• Deposit Date: May 9, 2023
• Journal: Journal of Nonlinear Science
• Print ISSN: 0938-8974
• Electronic ISSN: 1432-1467
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 27
• Issue: 5
• Pages: 1435-1461
• DOI: https://doi.org/10.1007/s00332-017-9366-5
• Keywords: Nonlinear elasticity; Geometric rigidity; Linearization; Crystals; Dislocations; Heterostructures
• Public URL: https://hull-repository.worktribe.com/output/4271039