An investigation of the comparative behaviour of alternative contact force models during elastic collisions

In this paper the rebound kinematics obtained using different contact force models are compared for the simple problem of an elastic sphere impacting obliquely with a target wall. It is shown that, for an appropriately calibrated normal spring stiffness and a realistic ratio of the tangential to normal spring stiffnesses, excellent results can be obtained by using a simple linear spring model. The paper also demonstrates that for non-linear contact models, integral equations for the tangential force–displacement cannot be used as the spring stiffness varies during the collision. Finally some comments are provided regarding the limitations of the linear spring model and alternatives are discussed.