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Updated: May 21, 2026

Development of an Experimental Setup for the Measurement of the Coefficient of Restitution under Vacuum Conditions

Development of an Experimental Setup for the Measurement of the Coefficient of Restitution under Vacuum Conditions

Published on: March 29, 2016

Negative coefficient of normal restitution.

Patric Müller¹, Dominik Krengel, Thorsten Pöschel

¹Institute for Multiscale Simulation, Universität Erlangen-Nürnberg, Nägelsbachstraße 49b, 91052 Erlangen, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 12, 2012

Summary

Negative coefficients of normal restitution are an inevitable consequence of finite interaction forces in particle collisions. This finding highlights a limitation of the commonly used hard sphere model, impacting granular physics simulations.

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Area of Science:

Physics
Materials Science
Granular Mechanics

Background:

The hard sphere model is widely used in granular physics simulations.
This model assumes instantaneous collisions and infinite interaction forces.
Existing models do not fully account for the complexities of real particle interactions.

Purpose of the Study:

To investigate the phenomenon of negative coefficients of normal restitution.
To identify the conditions under which negative restitution coefficients occur.
To highlight the limitations of the hard sphere model in describing particle collisions.

Main Methods:

Derivation of an explicit criterion for negative restitution coefficients.
Analysis of collision geometry and material properties.
Application of the criterion to linear dashpot and viscoelastic particle models.
Comparison with frictional particle interactions.

Main Results:

Negative coefficients of normal restitution are shown to be inevitable with finite interaction forces.
A criterion is derived that links material properties and collision geometry to negative restitution.
The phenomenon is demonstrated for linear dashpot and viscoelastic particles.
Frictional particles exhibit less pronounced negative restitution compared to smooth spheres.

Conclusions:

The widely used hard sphere model has an overlooked limitation due to the inevitability of negative restitution coefficients.
Finite interaction forces are critical in understanding particle collision dynamics.
The derived criterion provides a tool for predicting negative restitution in various material systems.