Rigid Body Motions and Local Compliance Response during Impact of Two Deformable Spheres

Abstract

The impact of two hard deformable spheres is revisited with the aim of investigating the constituent rigid body motions and indentation response of each sphere during collision. The latter are determined theoretically and the theoretical solutions are validated by comparing with numerical solutions of the coupled nonlinear dynamic models for impact of two hard deformable spheres. For elastic impact events, normalized tabulated solutions are derived using the Force Indentation Linearisation Method (FILM) and the tabulated solutions can be used to generate actual rigid body motions and indentation histories for each of the colliding spheres without need for numerical or finite element solutions. The analysis shows that the rigid body motion and local compliance response of each sphere depend on: (a) ratio of mass of sphere to effective mass of impact system, and (b) ratio of initial velocity of sphere to initial relative velocity of impact system. Finally, the 2-D collision problem is discussed and a simple procedure to determine the unique solution of all four unknowns is presented.