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.

Graphical AbstractFigure optionsDownload as PowerPoint slideResearch Highlights
► We examine oblique impacts of an elastic sphere with a planar target wall.
► The results obtained for four important classes of contact force models are compared.
► A linear spring can produce excellent agreement with much more complex models.
► If a nonlinear spring is used, the tangential force must be calculated incrementally.