The Mathematical Institute, University of Oxford, Eprints Archive

Riemann-Cartan Geometry of nonlinear dislocation mechanics

Yavari, A. and Goriely, A. (2011) Riemann-Cartan 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 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.

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:09 Feb 2012 13:50

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