TY - JOUR

T1 - Riemann-Cartan geometry of nonlinear disclination mechanics

AU - Yavari, A.

AU - Goriely, A.

N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK C1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2012/3/23

Y1 - 2012/3/23

N2 - 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).

AB - 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).

UR - http://hdl.handle.net/10754/599510

UR - http://journals.sagepub.com/doi/10.1177/1081286511436137

UR - http://www.scopus.com/inward/record.url?scp=84875834865&partnerID=8YFLogxK

U2 - 10.1177/1081286511436137

DO - 10.1177/1081286511436137

M3 - Article

SN - 1081-2865

VL - 18

SP - 91

EP - 102

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

IS - 1

ER -