Dynamic systems, and in particular mechanical structures, may be subjected to non-smooth loadings such as impacts or shocks. Moreover, their behavior itself may exhibit more or less non-smooth evolutions, as when fracture occurs. Therefore, robust simulation models are of interest to capture such behaviors. A particular focus is made herein on time-stepping 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 minimum number of numerical parameters. The original contributions of this article lie in the way the non-smooth behavior is formulated to be embedded in an explicit dynamics framework. This study focuses on the solver for dynamics with non-smooth interface behavior, rather than on the behavior models themselves. The applications concern non-smooth interface behaviors at macroscopic scale, between displacement jump on the 2D interface surface with no thickness, and interfacial force distributions acting on the bodies apart the interface. The proposed test cases which can serve as benchmarks for simulation codes, concern in a first step contact and perfectly plastic interface behavior (for illustrative purpose, on a 0D example). The last numerical test deals with contact, friction, fracture and adhesion for an extrinsic perfectly brittle interface behavior, to exemplify the feasibility on a full 3D finite element model.