Dynamical approach to weakly dissipative granular collisions

Granular systems present surprisingly complicated dynamics. In particular, nonlinear interactions and energy dissipation play important roles in these dynamics. Usually, constant coefficients of restitution are introduced phenomenologically to account for energy dissipation when grains collide. The...

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Bibliographic Details
Published in:arXiv.org 2014-08
Main Authors: Italo'Ivo Lima Dias Pinto, Rosas, Alexandre, Lindenberg, Katja
Format: Article
Language:English
Subjects:
Chaos theory
Collision dynamics
Energy dissipation
Equations of motion
Grains
Nonlinear dynamics
Numerical integration
Phenomenology
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Summary:Granular systems present surprisingly complicated dynamics. In particular, nonlinear interactions and energy dissipation play important roles in these dynamics. Usually, constant coefficients of restitution are introduced phenomenologically to account for energy dissipation when grains collide. The collisions are assumed to be instantaneous and to conserve momentum. Here, we improve on this phenomenology by introducing the dissipation through a viscous (velocity dependent) term in the equations of motion for two colliding grains. Using a first order approximation, we solve the equations of motion in the low viscosity regime. This approach allows us to calculate the collision time, the final velocity of each grain, and a coefficient of restitution that depends on the relative velocity of the grains. We compare our analytic results with those obtained by numerical integration of the equations of motion.
ISSN:2331-8422