Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

Handle URI:
http://hdl.handle.net/10754/599511
Title:
Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics
Authors:
Yavari, Arash; Goriely, Alain
Abstract:
We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan's moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.
Citation:
Yavari A, Goriely A (2012) Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics. Archive for Rational Mechanics and Analysis 205: 59–118. Available: http://dx.doi.org/10.1007/s00205-012-0500-0.
Publisher:
Springer Nature
Journal:
Archive for Rational Mechanics and Analysis
KAUST Grant Number:
KUKC1-013-04
Issue Date:
9-Mar-2012
DOI:
10.1007/s00205-012-0500-0
Type:
Article
ISSN:
0003-9527; 1432-0673
Sponsors:
A. YAVARI benefited from discussions with ARKADAS OZAKIN and AMIT ACHARYA. This publication was based on work supported in part by Award No KUKC1-013-04, made by King Abdullah University of Science and Technology (KAUST). A. YAVARI was partially supported by AFOSR-Grant No. FA9550-10-1-0378 and NSF-Grant No. CMMI 1042559.
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Full metadata record

DC FieldValue Language
dc.contributor.authorYavari, Arashen
dc.contributor.authorGoriely, Alainen
dc.date.accessioned2016-02-28T05:52:30Zen
dc.date.available2016-02-28T05:52:30Zen
dc.date.issued2012-03-09en
dc.identifier.citationYavari A, Goriely A (2012) Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics. Archive for Rational Mechanics and Analysis 205: 59–118. Available: http://dx.doi.org/10.1007/s00205-012-0500-0.en
dc.identifier.issn0003-9527en
dc.identifier.issn1432-0673en
dc.identifier.doi10.1007/s00205-012-0500-0en
dc.identifier.urihttp://hdl.handle.net/10754/599511en
dc.description.abstractWe present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan's moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.en
dc.description.sponsorshipA. YAVARI benefited from discussions with ARKADAS OZAKIN and AMIT ACHARYA. This publication was based on work supported in part by Award No KUKC1-013-04, made by King Abdullah University of Science and Technology (KAUST). A. YAVARI was partially supported by AFOSR-Grant No. FA9550-10-1-0378 and NSF-Grant No. CMMI 1042559.en
dc.publisherSpringer Natureen
dc.titleRiemann–Cartan Geometry of Nonlinear Dislocation Mechanicsen
dc.typeArticleen
dc.identifier.journalArchive for Rational Mechanics and Analysisen
dc.contributor.institutionGeorgia Institute of Technology, Atlanta, United Statesen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUKC1-013-04en
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