The Line-Tension Approximation as the Dilute Limit of Linear-Elastic Dislocations

@article{Conti2015TheLA,
  title={The Line-Tension Approximation as the Dilute Limit of Linear-Elastic Dislocations},
  author={Sergio Conti and Adriana Garroni and Michael Ortiz},
  journal={Archive for Rational Mechanics and Analysis},
  year={2015},
  volume={218},
  pages={699-755}
}
We prove that the classical line-tension approximation for dislocations in crystals, that is, the approximation that neglects interactions at a distance between dislocation segments and accords dislocations energy in proportion to their length, follows as the Γ-limit of regularized linear-elasticity as the lattice parameter becomes increasingly small or, equivalently, as the dislocation measure becomes increasingly dilute. We consider two regularizations of the theory of linear-elastic… 
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