Energy Dissipation in Normal Elastoplastic Impact Between Two Spheres

Abstract

Elastoplastic deformation occurs widely in engineering impact. Although many empirical solutions of elastoplastic impact between two spheres have been obtained, the analytical solution, verified by means of other methods, to the impact model has not been put forward. This paper proposes a dynamic pattern of elastoplastic impact for two spheres with low relative velocity, in which three stages are introduced and elastic and plastic regions are both considered. Finite element analyses with various parameters are carried out to validate the above model. The numerical results prove to agree with the theoretical predictions very well. Based on this model, the dissipation nature of elastoplastic impact are then analyzed, and the conclusion can be drawn that materials with lower yield strength, higher elastic modulus, and higher mass density have better attenuation and dissipation effects. The study provides a basis to predict the particle impact damping containing plastic deformation and to model the impact damped vibration system enrolling microparticles as a damping agent.

Modeling the fine particle impact damper

“…So it can be adaptable to different materials and dimensions of various spheres in collision. The model also has good precision, which has been verified by numerical simulations [40]. The greatest advantage of this model is that the velocities after impact can be obtained very quickly by the analytical solution, which is just the requirement from the numerical simulation for vibration system damped by impact damper in which numerous collisions occur.…”

“…Du and Wang [40] have proposed an analytical impact model for the collision between two different spheres. This model is simple and effective.…”

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

“…To illustrate elastoplastic impact analysis, the contact model of Du and Wang (2009) The rigid body displacements and constituent indentation responses are plotted in Figure 9 whereas the rigid body velocities and constituent indentation rates are plotted in Figure 10. The results predict that sphere 1 is displaced 44.61[ ] to the right of its initial position of contact (see Figure 9) and has a final velocity of 1.40[ / ] opposite to its initial velocity (see Figure 10), while sphere 2 is displaced 49.03[ ] to the right of its initial position of contact (see Figure 9) and has a final velocity of 0.54 [ / ] in the same direction as its initial velocity (see Figure 10).…”

“…The theoretical predictions obtained by Andrews (1930b) agreed with experiments to which they were compared. Du and Wang (2009) presented theoretical models for elastoplastic impact of two deformable spheres and used the models to predict the final velocities of the spheres after impact. Du and Wang (2009) validated their models using predictions from FE simulations.…”

“…Du and Wang (2009) presented theoretical models for elastoplastic impact of two deformable spheres and used the models to predict the final velocities of the spheres after impact. Du and Wang (2009) validated their models using predictions from FE simulations. The main limitation of the above theoretical studies is that they have been conducted only to determine the total compliance response without considering the constituent compliance response or rigid body motions.…”