A new model with uniform damping force for frictionless impacts with non-permanent deformation at the time of separation

This paper presents a new approach to modeling the contact force in continuous method of modeling an impact. This method considers the traditionally used Hertz spring force to represent the elastic behavior of the impact. A new nonlinear damping force is introduced to model the energy dissipation during the impact. Unlike the traditional spring-damping force elements used in some continuous contact force models, the introduced nonlinear damper can address impacts with non-permanent local deformation at the time of separation. We conduct both analytical and numerical investigations to mathematically express the damping factor as an explicit function of system parameters. In order to ensure that the presented force model can recover the desired restitution, an optimization approach is introduced and implemented to determine the optimal damping factor. The proposed force model is numerically verified on random systems. Finally, this new model is used to study the behavior of two colliding pendulums along with well-established piecewise and continuous approaches for modeling impacts.