Mechanics of Generalized Continua

One Hundred Years After the Cosserats

  • Gérard A. Maugin
  • Andrei V. Metrikine

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. On the Cosserat’s Works

    1. Front Matter
      Pages 1-1
    2. Marcelo Epstein
      Pages 15-24
  3. Cosserat Media (Rigidly Rotating Microstructure)

    1. Front Matter
      Pages 25-25
    2. Holm Altenbach, Victor A. Eremeyev
      Pages 27-35
    3. Arcady V. Dyskin, Elena Pasternak
      Pages 37-45
    4. Patrizio Neff, Jena Jeong, Ingo Münch, Hamidréza Ramézani
      Pages 55-63
    5. Wojciech Pietraszkiewicz, Victor A. Eremeyev
      Pages 79-86
    6. David A. Burton, Robin W. Tucker
      Pages 87-95
  4. Micromorphic Media (Deformable Microstructure)

    1. Front Matter
      Pages 97-97
    2. Ralf Jänicke, Stefan Diebels
      Pages 99-107
    3. James D. Lee, Youping Chen, Xianqiao Wang
      Pages 109-117
  5. From the Discrete to the Continuum Description (Cosserat and Other Continua Often in Relation to Dynamical Properties, Homogenization)

    1. Front Matter
      Pages 119-119
    2. Claude Boutin, Stéphane Hans, Céline Chesnais
      Pages 131-141
    3. Vladimir I. Erofeyev, Elena A. Nikitina, Alla V. Sharabanova
      Pages 143-148
    4. Andrei V. Metrikine, Julia M. Prokhorova
      Pages 149-160
    5. Alexey V. Porubov, Eron L. Aero, B. R. Andrievsky
      Pages 161-168
    6. Holger Steeb, Marcel Frehner, Stefan Schmalholz
      Pages 179-187
  6. Gradient Theory (Weakly Nonlocal Theories)

    1. Front Matter
      Pages 189-189
    2. Francesco Froiio, A. Zervos, Ioannis Vardoulakis
      Pages 211-221
  7. Complex Structured Media (Often with Application to Dislocations)

    1. Front Matter
      Pages 233-233
    2. Robert H. J. Peerlings, Y. Kasyanyuk, A. Roy, M. G. D. Geers
      Pages 245-250
  8. Numerical Problems

    1. Front Matter
      Pages 251-251
    2. Stefanos-Aldo Papanicolopulos, A. Zervos, Ioannis Vardoulakis
      Pages 269-277
    3. Paul Fischer, Julia Mergheim, Paul Steinmann
      Pages 279-286
    4. Carlo Sansour, Sebastian Skatulla, A. Arunachalakasi
      Pages 287-294
  9. Beyond the Cosserats: Original Approaches (Kinematics, Geometry, Fractals)

    1. Front Matter
      Pages 295-295
    2. Wolfgang Muschik, Christina Papenfuss
      Pages 307-314
    3. Jun Li, Martin Ostoja-Starzewski
      Pages 315-323

About this book


In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers.

The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics. The diverse topics covered include: the properties of Cosserat media, micromorphic bodies, micropolar solids and fluids, weakly- and strongly-nonlocal theories, gradient theories of elasticity and plasticity, defect theory, everywhere-defective materials, bodies with fractal structure, as well as other related topics. 

Key features:

- Focuses on recent developments in continuum mechanics and materials design, including numerical examples and newly developed models.

- Presents numerical examples to demonstrate the efficiency of various solution techniques.

- Provides a unique overview of generalized continuum mechanics, illustrating the important applications of this theory in various other scientific disciplines.

- Includes a foreword written by renowned physicist and materials scientist A.C. Eringen.

Mechanics of Generalized Continua can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.


Contact Mechanics Cosserats Deformation Mechanics Generalized Continua Materials Science Vibration continuum mechanics geometry mechanical engineering mechanics model modeling plasticity porous media

Editors and affiliations

  • Gérard A. Maugin
    • 1
  • Andrei V. Metrikine
    • 2
  1. 1.Institut Jean Le Rond d'AlembertUniversité Paris VIParis CX 5France
  2. 2.Faculty of Civil Engineering andDelft University of Technology,DelftNetherlands

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