International audienceA model is presented that accurately describes brittle failure in the presence of cohesive forces, with a particular focus on the prediction of non planar crack paths. In comparison with earlier literature, the originality of the procedure lies in the a posteriori computation of the crack advance from the equilibrium, instead of a most common determination beforehand from the stress state ahead of the front. To this aim, a robust way of introducing brittle non-smooth cohesive laws in the X-FEM is presented. Then the a posteriori update algorithm of the crack front is detailed. The crack deflection angle is computed from cohesive quantities exclusively, by introducing equivalent stress intensity factors. The procedure shows good accordance with experiments from the literature