Multibody models are often coupled with other domains in order to enlarge the scope of computer-based analysis. In particular, modeling multibody systems (MBSs) in interaction with granular media is of great interest for industrial process such as railway track maintenance, handling of aggregates, etc. This paper presents a strong coupling methodology for unifying a multibody formalism using relative coordinates and a discrete element method based on non-smooth contact dynamics (NSCD). Both tree-like and closed-loop MBSs are considered. For the latter, the coordinate partitioning techniques is applied in the NSCD framework. The proposed approach is applied on the slider-crank mechanism benchmark. Results are in very good agreement with results obtained with other techniques from the literature. Finally, a multibody model of a tamping machine is coupled to a discrete element model of railway ballast in order to analyse efficiency of track maintenance. This application demonstrates that the dynamics of the machine must be taken into account so as to estimate the performance of the maintenance process correctly.