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.
|Original language||American English|
|Number of pages||28|
|Journal||Proceedings of the Royal Society of Edinburgh Section A: Mathematics|
|State||Published - 1 Aug 2016|
Bibliographical notePublisher Copyright:
© Copyright 2016 Royal Society of Edinburgh.
- Gromov-Hausdorff convergence
- Weitzenböck manifolds