Type
ArticleAuthors
Yavari, A.Goriely, A.
KAUST Grant Number
KUK C1-013-04Date
2012-03-23Online Publication Date
2012-03-23Print Publication Date
2013-01Permanent link to this record
http://hdl.handle.net/10754/599510
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Show full item recordAbstract
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.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.Publisher
SAGE Publicationsae974a485f413a2113503eed53cd6c53
10.1177/1081286511436137