The use of a 3D discrete element method (DEM) is proposed to study concrete submitted to dynamic loading. The model has already been validated through quasi-static simulations. This paper aims first at extending the validation of the model and at contributing to the understanding of the physical mechanisms in stake. Once the correct quasi-static identification of the model parameters is done, compressive dynamic tests are first simulated. Unchanged, the model proves able to reproduce the concrete strain rate dependency, and confirms the inertia-based hypothesis at high strain rates. Dynamic tensile tests show that a local rate effect has to be introduced to reproduce the experimental rate dependency, which would then be a material-intrinsic effect.