Abstracts Physics

Rebound predictions of mechanical collisions

by Liang-Ju Lai

Predictions of mechanical collisions between two bodies frequently cannot be completed by the impulse-momentum equation together with a complete description of the motion of the system at the initial contact. Additional account must be taken of the deformations and frictional interaction induced by the impulsive reaction force, where the bodies contact one another, as these play an important role in the outcome of the collision. During the time the bodies are in contact, elastic, friction and inertia properties combine to produce a complex variation of sliding and sticking through out the contact surface. For accurately predicting the impulse and velocity changes during contact, a considerably simplified, coupled, conservative model, which captures the essential characteristics of the elastic-friction interaction during contact loading, is investigated in this thesis. In this simplified model, the interface between two colliding bodies resembles the behavior of a pair of mutually perpendicular, non-linear springs which react independently with the exception that the stiffness of the tangential "spring" is influenced by the normal displacement. These elastic properties, in combination with inertial properties derived from generalized impulse-momentum laws, form a "spring-mass" system for which numerical integration yields the prediction of rebound velocities. For comparison, an explicit non-linear finite element code, DYNA3D, developed at Lawrence Livermore National Laboratory for analyzing the transient dynamic response of three-dimensional solids, is used to predict the responses of an elastic sphere and elastic rod, each colliding with a rigid plane with varying initial velocities and configurations. Results are also compared with results of a complex analysis of collisions of spheres by Maw, Barber, and Fawcett (1976).