Dynamic systems, and in particular mechanical structures, may be subjected to non-smooth loadings such as impacts or shocks. Moreover, their behavior may itself exhibit more or less non-smooth behaviors, as when fracture occurs. Therefore, robust simulation models are of interest to capture such behaviors. A particular focus is made herein on explicit dynamics schemes to allow efficient simulations, and non-smoothness is embedded within the discrete resolution model, so that robust simulations can be obtained, with a minimal number of numerical parameters. The applications concern non-smooth interface behaviors, are illustrated on simple test cases, and feasibility is shown on a full 3D finite element model.