Shock dynamics in granular chains: numerical simulations and comparison with experimental tests

Ngoc-Son Nguyen 1 Bernard Brogliato 1
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : The aim of this work is to simulate shock dynamics in granular chains of balls using the LZB multiple impact model and compare the numerical results to the experimental results available in the literature. The LZB model has been introduced to solve the multiple impact problem that arises in the rigid body systems when multiple contacts collide at the same time. The Darboux-Keller dynamics is considered in this model to change the time scale to the impulse scale. The interaction at the contact points is modeled by compliance contact laws. The energy dissipation at the contact points during the impact process, resulting from complex phenomena such as the plasticity, the viscosity, the noise, the vibration, etc., is taken into account by using Stronge's energetic coefficient of restitution. The coupling between various contact points, due to the wave effects, is described by a distributing law that relates the impulse change at one contact to that at another contact depending on their relative stiffness and their relative potential energy. The LZB model is then coupled to the event-driven scheme in order to simulate the motion of the nonsmooth mechanical systems. Different kinds of granular chains are investigated: monodisperse chains, i.e. chains of identical balls; tapered chains, i.e. chains composed of balls with decreasing size; stepped chains, i.e. chains composed of a large monodisperse section followed by a small monodisperse section. Particular attention is paid to the dispersion effect and the wave propagation in the tapered chains, to the interaction of two solitary waves in the monodisperse chains, and to the formation of a solitary wave train (a set of single solitary waves with decreasing amplitudes) in the stepped chains. Comparison with the experimental results shows that the numerical simulations with the LZB multiple impact model reproduce very well the experimental observations.
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https://hal.inria.fr/inria-00597468
Contributor : Ngoc-Son Nguyen <>
Submitted on : Wednesday, June 1, 2011 - 9:25:58 AM
Last modification on : Thursday, February 7, 2019 - 5:28:43 PM
Long-term archiving on : Friday, September 2, 2011 - 2:21:49 AM

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Ngoc-Son Nguyen, Bernard Brogliato. Shock dynamics in granular chains: numerical simulations and comparison with experimental tests. [Research Report] RR-7636, INRIA. 2011. ⟨inria-00597468⟩

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