In this talk I will introduce a model for linear elasticity on deformations showing cracks. The elastic energy plus a penalization energy of the fractured zone due to the atomic interaction is considered and a Gamma convergence result for this is enstablished, showing the arising of topological singularities in an otherwise perfect lattice. The approach is reminescent of the one for Ginzburg Landau and screw dislocations models, but avoiding the core radius technique. To deal with this a new general notion of distributional determinant for BV maps is introduced.