  We propose nonlinear semi-discrete and discrete models for the elastic energy
induced by a finite systems of edge dislocations in two dimensions. Within the
dilute regime, we analyze the asymptotic behavior of the nonlinear elastic
energy, as the core-radius (in the semi-discrete model) and the lattice spacing
(in the purely discrete one) vanish. Our analysis passes through a
linearization procedure within the rigorous framework of Gamma-convergence.
