In this talk we analyse the Γ-convergence of a family of nonlocal functionals defined on finite-differences to a local functional F(u) that depends on the symmetric gradient of u and on the jump set of u. This is a generalisation to the Griffith functional of a classical result for the Mumford-Shah of Gobbino. The key step is the compactness in GSBD of sequences with uniformly bounded energy without any additional L∞-bound. This is a work in collaboration with S. Almi, E. Davoli and E. Tasso.