Vol. 11, No. 2, 2016

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A simple hard-particle collision model with a smooth transition to full slip

M. B. Rubin

Vol. 11 (2016), No. 2, 137–155

Hard-particle models assume that the collision between rigid bodies is instantaneous and they propose algebraic equations for the jumps in the motions of the rigid bodies based on an assumed functional form for the impulsive force acting during the collision process. These hard-particle models have the advantage that they are significantly less computationally expensive than soft-particle models. Moreover, they are sufficiently accurate for some applications and can also be used for preliminary analysis of complicated processes with large numbers of particle interactions. Here, a simple three parameter hard-particle collision model is developed which predicts a smooth transition from normal collisions with no slip to oblique collisions with full slip. This model automatically satisfies a number of physical restrictions on the impulsive force. An additional physical restriction on non-negative energy dissipation places nontrivial restrictions on the model parameters. Examples show the importance of improved modeling of the transition region from normal to oblique collisions with full slip.

coefficient of restitution, collision, friction, hard-particle, rigid bodies, spheres
Received: 23 May 2015
Accepted: 20 September 2015
Published: 23 February 2016
M. B. Rubin
Faculty of Mechanical Engineering
Technion - Israel Institute of Technology
32000 Haifa