Reference motion in deformable bodies under rigid body motion and vibration. Part II: evaluation of the coefficient of restitution for impacts

The dynamic analysis of rigid body impacts is usually performed by using the coefficient of restitution as a measure of the mechanical energy lost in the process. The coefficient of restitution provides an algebraic equation that allows impulse–momentum balance equations to be solved. This paper reports a method for calculating the kinematic coefficient of restitution for the impact of deformable bodies by using a numerical simulation procedure. Calculations were done within the framework of the floating reference frame approach. As shown here for the first time, discriminating between reference velocities and rigid body equivalent velocities is essential with a view to accurately calculating the kinematic coefficient of restitution. Thus, the velocities at which the contact points approach and depart must be calculated as rigid body equivalent velocities. If references velocities are used instead, the resulting coefficient of restitution lacks physical significance. The proposed method is illustrated with two applications, namely: an axial impact of a rigid body on a deformable rod and a transverse impact of a beam on a fixed stop.