Boundary-layer analysis of a pile-up of walls of edge dislocations at a lock

@article{Garroni2015BoundarylayerAO,
  title={Boundary-layer analysis of a pile-up of walls of edge dislocations at a lock},
  author={Adriana Garroni and Patrick van Meurs and Mark A. Peletier and Lucia Scardia},
  journal={arXiv: Analysis of PDEs},
  year={2015}
}
In this paper we analyse the behaviour of a pile-up of vertically periodic walls of edge dislocations at an obstacle, represented by a locked dislocation wall. Starting from a continuum non-local energy $E_\gamma$ modelling the interactions$-$at a typical length-scale of $1/\gamma$$-$of the walls subjected to a constant shear stress, we derive a first-order approximation of the energy $E_\gamma$ in powers of $1/\gamma$ by $\Gamma$-convergence, in the limit $\gamma\to\infty$. While the zero… 

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