Riemann-Cartan geometry of nonlinear disclination mechanics

Handle URI:
http://hdl.handle.net/10754/599510
Title:
Riemann-Cartan geometry of nonlinear disclination mechanics
Authors:
Yavari, A.; Goriely, A.
Abstract:
In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan's method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).
Citation:
Yavari A, Goriely A (2012) Riemann-Cartan geometry of nonlinear disclination mechanics. Mathematics and Mechanics of Solids 18: 91–102. Available: http://dx.doi.org/10.1177/1081286511436137.
Publisher:
SAGE Publications
Journal:
Mathematics and Mechanics of Solids
KAUST Grant Number:
KUK C1-013-04
Issue Date:
23-Mar-2012
DOI:
10.1177/1081286511436137
Type:
Article
ISSN:
1081-2865; 1741-3028
Sponsors:
This publication was based on work supported in part by Award No KUK C1-013-04, made by King Abdullah University of Science and Technology (KAUST). AG is a Wolfson Royal Society Merit Holder. AY was partially supported by NSF-Grant No. CMMI 1042559.
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Full metadata record

DC FieldValue Language
dc.contributor.authorYavari, A.en
dc.contributor.authorGoriely, A.en
dc.date.accessioned2016-02-28T05:52:29Zen
dc.date.available2016-02-28T05:52:29Zen
dc.date.issued2012-03-23en
dc.identifier.citationYavari A, Goriely A (2012) Riemann-Cartan geometry of nonlinear disclination mechanics. Mathematics and Mechanics of Solids 18: 91–102. Available: http://dx.doi.org/10.1177/1081286511436137.en
dc.identifier.issn1081-2865en
dc.identifier.issn1741-3028en
dc.identifier.doi10.1177/1081286511436137en
dc.identifier.urihttp://hdl.handle.net/10754/599510en
dc.description.abstractIn the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan's method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).en
dc.description.sponsorshipThis publication was based on work supported in part by Award No KUK C1-013-04, made by King Abdullah University of Science and Technology (KAUST). AG is a Wolfson Royal Society Merit Holder. AY was partially supported by NSF-Grant No. CMMI 1042559.en
dc.publisherSAGE Publicationsen
dc.subjectDifferential geometryen
dc.subjectDisclinationsen
dc.subjectGeometric elasticityen
dc.subjectResidual stressesen
dc.titleRiemann-Cartan geometry of nonlinear disclination mechanicsen
dc.typeArticleen
dc.identifier.journalMathematics and Mechanics of Solidsen
dc.contributor.institutionGeorgia Institute of Technology, Atlanta, United Statesen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK C1-013-04en
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