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dc.contributor.authorYavari, A.
dc.contributor.authorGoriely, A.
dc.date.accessioned2016-02-28T05:52:29Z
dc.date.available2016-02-28T05:52:29Z
dc.date.issued2012-03-23
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.
dc.identifier.issn1081-2865
dc.identifier.issn1741-3028
dc.identifier.doi10.1177/1081286511436137
dc.identifier.urihttp://hdl.handle.net/10754/599510
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).
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.
dc.publisherSAGE Publications
dc.subjectDifferential geometry
dc.subjectDisclinations
dc.subjectGeometric elasticity
dc.subjectResidual stresses
dc.titleRiemann-Cartan geometry of nonlinear disclination mechanics
dc.typeArticle
dc.identifier.journalMathematics and Mechanics of Solids
dc.contributor.institutionGeorgia Institute of Technology, Atlanta, United States
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
kaust.grant.numberKUK C1-013-04
dc.date.published-online2012-03-23
dc.date.published-print2013-01


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