Yavari, A. and Goriely, A. (2011) RiemannCartan Geometry of nonlinear dislocation mechanics. Archive for Rational Mechanics and Analysis . (Submitted)

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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 Weitzenbock manifold, i.e. a manifold with a flat affine connection with torsion but vanishing nonmetricity. 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 nontrivial examples of zerostress 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.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1444 
Deposited By:  Peter Hudston 
Deposited On:  18 Nov 2011 07:45 
Last Modified:  29 May 2015 19:08 
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