We show how a two-scales FE model—within a sequential approach—leads to consistently simulate the DEF macroscopic consequences: cracks pattern and opening, residual modulus decrease. The mesoscopic part of this model is adapted to heterogeneous materials and is based on two kinematics enrichments. The first one leads to a very fast meshing process along the randomly chosen set of aggregates and, the second leads to directly compute the cracks openings. Assuming DEF is driving to a progressive and homogeneous mortar expansion, we show how the macroscopic—concrete—expansion as well the cracks pattern are consistent with the experiments. For the latter we are interested in the characterization of the aggregates effect on the amplitude of DEF swelling, so that we focus on parameters such as the size and the volume fraction of granular inclusions.