  We wish to understand the macroscopic plastic behaviour of metals by
upscaling the micro-mechanics of dislocations. We consider a highly simplified
dislocation network, which allows our microscopic model to be a one dimensional
particle system, in which the interactions between the particles (dislocation
walls) are singular and non-local.
  As a first step towards treating realistic geometries, we focus on
finite-size effects rather than considering an infinite domain as typically
discussed in the literature. We derive effective equations for the dislocation
density by means of \Gamma-convergence on the space of probability measures.
Our analysis yields a classification of macroscopic models, in which the size
of the domain plays a key role.
