Multiple Impacts in Dissipative Granular Chains

  • Ngoc Son Nguyen
  • Bernard Brogliato

Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 72)

Table of contents

  1. Front Matter
    Pages 1-18
  2. Ngoc Son Nguyen, Bernard Brogliato
    Pages 1-9
  3. Ngoc Son Nguyen, Bernard Brogliato
    Pages 11-29
  4. Ngoc Son Nguyen, Bernard Brogliato
    Pages 31-69
  5. Ngoc Son Nguyen, Bernard Brogliato
    Pages 71-107
  6. Ngoc Son Nguyen, Bernard Brogliato
    Pages 109-157
  7. Ngoc Son Nguyen, Bernard Brogliato
    Pages 159-194
  8. Back Matter
    Pages 195-232

About this book


The extension of collision models for single impacts between two bodies, to the case of multiple impacts (which take place when several collisions occur at the same time in a multibody system) is a challenge in Solid Mechanics, due to the complexity of such phenomena, even in the frictionless case. This monograph aims at presenting the main multiple collision rules proposed in the literature. Such collisions typically occur in granular materials, the simplest of which are made of chains of aligned balls. These chains are used throughout the book to analyze various multiple impact rules which extend the classical Newton (kinematic restitution), Poisson (kinetic restitution) and Darboux-Keller (energetic or kinetic restitution) approaches for impact modelling. The shock dynamics in various types of chains of aligned balls (monodisperse, tapered, decorated, stepped chains) is carefully studied and shown to depend on several parameters: restitution coefficients, contact stiffness ratios, elasticity coefficients (linear or nonlinear force/ indentation relation), and kinetic angles (that depend on the mass ratios). The dissipation and the dispersion of kinetic energy during a multiple impact are mandatory modelling, and are quantified with suitable indices. Particular attention is paid to the ability of the presented laws to correctly predict the wave effects in the chains. Comparisons between many numerical and experimental results are shown, as well as comparisons between four different impact laws in terms of their respective abilities to correctly model dissipation and dispersion of energy.


Binary Collisions Dissipative Granular Chains Frémond Approach Generalized Kinematic Law Han-Gilmore Approach LZB Model Multiple Impact Laws Pfeiffer-Glocker Model

Authors and affiliations

  • Ngoc Son Nguyen
    • 1
  • Bernard Brogliato
    • 2
  1. 1., InovalléeINRIASaint-Ismier cedexFrance
  2. 2., InovalléeINRIASaint-Ismier cedexFrance

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-642-39297-9
  • Online ISBN 978-3-642-39298-6
  • Series Print ISSN 1613-7736
  • Series Online ISSN 1860-0816
  • Buy this book on publisher's site