Riemannian surfaces with torsion as homogenization limits of locally Euclidean surfaces with dislocation-type singularities
Published online by Cambridge University Press: 01 July 2016
Extract
We reconcile two classical models of edge dislocations in solids. The first, from the early 1900s, models isolated edge dislocations as line singularities in locally Euclidean manifolds. The second, from the 1950s, models continuously distributed edge dislocations as smooth manifolds endowed with non-symmetric affine connections (equivalently, endowed with torsion fields). In both models, the solid is modelled as a Weitzenböck manifold. We prove, using a weak notion of convergence, that the second model can be obtained rigorously as a homogenization limit of the first model as the density of singular edge dislocation tends to infinity.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 4 , August 2016 , pp. 741 - 768
- Copyright
- Copyright © Royal Society of Edinburgh 2016
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