The contact between particles is an important task in simulating the behaviour of particle assemblies. Conventionally, the dissipative contribution to the normal contact force is described by viscoelastic damping, where the concept of the constant coefficient of restitution (COR) is extensively explored in Discrete Element Method (DEM) simulations. From the previous studies it is known that different models provide different time-histories during the contact even for the equal values of the COR.In the present investigation, a comparative study of various nonlinear damping models for spherical particles is given on the basis of dimensional analysis. The research aims to demonstrate how the differences observed in a single particle collision contribute to the collective behaviour of particles in multi-particle systems and thereby affect the sensitivity of DEM results for various damping models. The selected samples of 3D granular flows have been solved numerically to illustrate the contribution of the damping models to the dynamic behaviour during the impact. The current report presents the results obtained in studying the behaviour of particles during the filling of a hopper, the discharge and the motion of the particles on the bottom-plane of a rectangular box. Moreover, the most popular nonlinear damping models reported by Lee and Herrmann, Brilliantov, Tsuji and modified Tsuji models have been examined. The results of the present study allow us to define basic tendencies observed, when various models are applied.