Theoretical investigation on the contact duration in elastic and inelastic collision of a circular plate to a planar surface

In this paper a new theoretical method is proposed for calculating the normalized contact duration and indentation depth in elastic, elastic-plastic and plastic collision of circular plates. The contact duration is composed of total loading time and unloading time that are dependent on the relationship between the interaction force and normal indentation. For plastic collision, the contact duration relates to the coefficient of restitution (COR) of the collision. Considering the actual thickness of a circular plate, a coefficient of indentation (COI) is newly introduced in theoretical analyses of the COR. According to experimental results of COR, a hybrid nonlinear model is also proposed to describe the COR of circular plates for obtaining the unloading time of the plastic collision. Contact force history during collision can be expressed approximately by a half-sine wave and the force and contact duration is calculated numerically.