On the adaptation of local impact laws for multiple impact problems

Abstract

The classical local impact laws of Newton and Poisson are able to capture the behaviour observed in single-impact collisions in many situations. However, in the case of collisions with multiple impacts, the simultaneous enforcement of local impact laws does not reproduce essential features of the physical process, such as propagation effects. The aim of this work is to broaden the applicability of the classical Newton impact law to problems involving multiple impacts by assuming instantaneous local impact times and a rigid behaviour of the bodies in contact. The proposed method is implemented as an extension of the nonsmooth generalized-α method. In order to model events involving multiple impacts, a sequence of impact problems is defined on a vanishing time interval and the active set of each velocity-level sub-problem is redefined in such a way that closed contacts with zero pre-impact velocity are considered inactive. This simple redefinition allows us to deal successfully with many situations involving multiple impacts, by generating a sequence of impact problems which is amenable to be modelled by the simultaneous enforcement of classical impact laws. Additionally, the methodology fits well under the algorithmic structure of the nonsmooth generalized-α scheme or any scheme dealing with linear complementary problems at velocity level. Several examples are analyzed in order to assess the performance of the method and to discuss its main features.