Front migration for the dislocation strain in single crystals
type: Item
instance of: scholarly article
title: Front migration for the dislocation strain in single crystals
zbMATH Open document ID: 1394.35499
published in: Communications in Mathematical Sciences
publication date: 2018-04-06T00:00:00Z
review text: A single crystal is considered, i.e., a smooth 3-D elastic body containing a high density of point-defects and dislocations. In particular, the author considers prismatic dislocation loops which result as the primary manifestation of irradiated or highly-deformed crystals. He considers linearized elasticity and identifies the macroscopic dislocation-induced strain and its trace, directly related to the presence of dislocations, as the basic model variables. Further, he relies on a previously-introduced tensor version of a Cahn-Hilliard system in the context of incompatible linearized elasticity and considers the point-defects collapse into prismatic loops, yielding some well-formed microstructure. By means of a formal asymptotic analysis, he determines the front dynamics and obtains as a result a tensor version of Mullins-Sekerka dynamics. The associated gradient-flow formalism is also investigated.
reviewed by: Dongbing Zha
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35G31
Mathematics Subject Classification ID: 35J48
Mathematics Subject Classification ID: 35J50
Mathematics Subject Classification ID: 35K52
Mathematics Subject Classification ID: 74B10
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 6856593
zbMATH Keywords: dislocations
zbMATH Keywords: linear elasticity
zbMATH Keywords: incompatibility
zbMATH Keywords: Cahn-Hilliard system
zbMATH Keywords: evolution law
zbMATH Keywords: second principle
author: N. Van Goethem
MaRDI profile type: Publication
DOI: 10.4310/CMS.2017.V15.N7.A3
description: scientific article; zbMATH DE number 6856593