In this talk, we show that E. De Giorgi’s conjecture for the nonlocal approximation of freediscontinuity problems extends to the case of functionals defined in terms of the symmetric gradient of the admissible field. After introducing a suitable class of continuous finite-difference approximants, we prove the compactness of eformations with equibounded energies, as well as their Gamma-convergence. The compactness analysis relies on a generalization of a Fr ́echet-Kolmogorov approach. An essential difficulty is the identification of the limiting space of admissible deformations. We show that if the approximants involve superlinear contributions, a limiting GSBD representation can be ensured, whereas a further integral geometric term appears in the limiting functional in the linear case. We eventually discuss the connection between this latter setting and an open problem in the theory of integral geometric measures.