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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 59-118 |
| Number of pages | 60 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 205 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 9 2012 |
| Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUKC1-013-04
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.