Lecture Notes in Applied and Computational Mechanics

Multiple Impacts in Dissipative Granular Chains

Authors: Nguyen, Ngoc Son, Brogliato, Bernard

  • Presents generalities about multiple impacts  incl. definition, discrepancy with respect to single impacts, various classes of models for impacts, etc
  • Emphasis on granular chains of aligned balls, which is a topic of interest for both mechanicians and physicists working on granular matter, and more generally to anyone interested in complex impacts phenomena
  • Includes an experimental validation of the LZB model and wave propagation in granular chains
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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.

Table of contents (6 chapters)

  • Introduction

    Nguyen, Ngoc Son (et al.)

    Pages 1-9

  • Multiple Impacts in Granular Chains

    Nguyen, Ngoc Son (et al.)

    Pages 11-29

  • Rigid-Body Multiple Impact Laws

    Nguyen, Ngoc Son (et al.)

    Pages 31-69

  • LZB Multiple Impact Model

    Nguyen, Ngoc Son (et al.)

    Pages 71-107

  • Analysis and Validation of the LZB Model

    Nguyen, Ngoc Son (et al.)

    Pages 109-157

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-39298-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-642-39297-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover n/a
  • ISBN 978-3-642-43775-5
  • Free shipping for individuals worldwide
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Multiple Impacts in Dissipative Granular Chains
Authors
Series Title
Lecture Notes in Applied and Computational Mechanics
Series Volume
72
Copyright
2014
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-39298-6
DOI
10.1007/978-3-642-39298-6
Hardcover ISBN
978-3-642-39297-9
Softcover ISBN
978-3-642-43775-5
Series ISSN
1613-7736
Edition Number
1
Number of Pages
XX, 234
Topics