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Cosserat Continuum Mechanics

With Applications to Granular Media

  • Ioannis Vardoulakis

Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 87)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Ioannis Vardoulakis
    Pages 1-3
  3. Ioannis Vardoulakis
    Pages 5-32
  4. Ioannis Vardoulakis
    Pages 33-57
  5. Ioannis Vardoulakis
    Pages 59-73
  6. Ioannis Vardoulakis
    Pages 75-87
  7. Ioannis Vardoulakis
    Pages 89-97
  8. Ioannis Vardoulakis
    Pages 99-119
  9. Ioannis Vardoulakis
    Pages 121-150
  10. Ioannis Vardoulakis
    Pages 151-179

About this book

Introduction

This textbook explores the theory of Cosserat continuum mechanics, and covers fundamental tools, general laws and major models, as well as applications to the mechanics of granular media. While classical continuum mechanics is based on the axiom that the stress tensor is symmetric, theories such as that expressed in the seminal work of the brothers Eugène and François Cosserat are characterized by a non-symmetric stress tensor. The use of von Mises motor mechanics is introduced, for the compact mathematical description of the mechanics and statics of Cosserat continua, as the Cosserat continuum is a manifold of oriented “rigid particles” with 3 dofs of displacement and 3 dofs of rotation, rather than a manifold of points with 3 dofs of displacement. Here, the analysis is restricted to infinitesimal particle displacements and rotations. This book is intended as a valuable supplement to standard Continuum Mechanics courses, and graduate students as well as researchers in mechanics and applied mathematics will benefit from its self-contained text, which is enriched by numerous examples and exercises.    

Keywords

Granular Physics Cosserat Theory Motor Calculus Non-simple Continua Continuum Mechanics Model Granular Flow Cosserat Fluids Local Kinematics Elastic Solids Micropolar Mechanics Micropolar Elasticity Granular Materials

Authors and affiliations

  • Ioannis Vardoulakis
    • 1
  1. 1.National Technical University of Athens AthensGreece

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-95156-0
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-95155-3
  • Online ISBN 978-3-319-95156-0
  • Series Print ISSN 1613-7736
  • Series Online ISSN 1860-0816
  • Buy this book on publisher's site
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