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The Mechanics of Ribbons and Möbius Bands

  • Book
  • © 2016

Overview

Editors:
  1. Roger Fosdick

    1. Aeropsace Engineering and Mechanics, University of Minnesota, Minneapolis, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Eliot Fried

    1. Okinawa Institute of Science and Technol Mathematical Soft Matter Unit, Okinawa, Japan

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Authoritative English translations of three seminal, but little known, papers on the topic
  • Original research papers by contemporary authorities on the topic
  • Cross-cutting connections between the fields of geometry, mechanics, biology, and nanotechnology
  • Comprehensive introduction written by editors

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Table of contents (18 chapters)

  1. Front Matter

    Pages I-VI
    Download chapter PDF

  2. Foreword

    • Roger Fosdick, Eliot Fried
    Pages 1-2

  3. Translation of Michael Sadowsky’s Paper “An Elementary Proof for the Existence of a Developable Möbius Band and the Attribution of the Geometric Problem to a Variational Problem”

    • Denis F. Hinz, Eliot Fried
    Pages 3-6

  4. Translation and Interpretation of Michael Sadowsky’s Paper “Theory of Elastically Bendable Inextensible Bands with Applications to the Möbius Band”

    • Denis F. Hinz, Eliot Fried
    Pages 7-17

  5. Translation of Michael Sadowsky’s Paper “The Differential Equations of the Möbius Band”

    • Denis F. Hinz, Eliot Fried
    Pages 19-22

  6. Translation of W. Wunderlich’s “On a Developable Möbius Band”

    • Russell E. Todres
    Pages 23-34

  7. Gamma-Limit of a Model for the Elastic Energy of an Inextensible Ribbon

    • Nicholas O. Kirby, Eliot Fried
    Pages 35-47

  8. “Wunderlich, Meet Kirchhoff”: A General and Unified Description of Elastic Ribbons and Thin Rods

    • Marcelo A. Dias, Basile Audoly
    Pages 49-66

  9. Equilibrium Shapes with Stress Localisation for Inextensible Elastic Möbius and Other Strips

    • E. L. Starostin, G. H. M. van der Heijden
    Pages 67-112

  10. Bending Paper and the Möbius Strip

    • Sören Bartels, Peter Hornung
    Pages 113-136

  11. Roadmap to the Morphological Instabilities of a Stretched Twisted Ribbon

    • Julien Chopin, Vincent Démery, Benny Davidovitch
    Pages 137-189

  12. The Shrinking Figure Eight and Other Solitons for the Curve Diffusion Flow

    • Maureen Edwards, Alexander Gerhardt-Bourke, James McCoy, Glen Wheeler, Valentina-Mira Wheeler
    Pages 191-211

  13. Kinematical Aspects of Levi-Civita Transport of Vectors and Tensors Along a Surface Curve

    • James Casey
    Pages 213-249

  14. Non-Euclidean Ribbons

    • Efi Efrati
    Pages 251-261

  15. The Second-Order \(L^{2}\)-Flow of Inextensible Elastic Curves with Hinged Ends in the Plane

    • Chun-Chi Lin, Yang-Kai Lue, Hartmut R. Schwetlick
    Pages 263-291

  16. Buckling of Naturally Curved Elastic Strips: The Ribbon Model Makes a Difference

    • Basile Audoly, Keith A. Seffen
    Pages 293-320

  17. Residual Stresses and Poisson’s Effect Drive Shape Formation and Transition of Helical Structures

    • Zi Chen, Xiaomin Han, Huang Zheng
    Pages 321-333

  18. Representation for a Smooth Isometric Mapping from a Connected Planar Domain to a Surface

    • Yi-Chao Chen, Roger Fosdick, Eliot Fried
    Pages 335-350

  19. Erratum to: Four Papers Published in the Journal of Elasticity (2015) 119(1–2)

    • Roger Fosdick, Eliot Fried
    Pages 351-352
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Keywords

About this book

Recent developments in biology and nanotechnology have stimulated a rapidly growing interest in the mechanics of thin, flexible ribbons and Mobius bands.

This edited volume contains English translations of four seminal papers on this topic, all originally written in German; of these, Michael A. Sadowsky published the first in 1929, followed by two others in 1930, and Walter Wunderlich published the last in 1962.

The volume also contains invited, peer-reviewed, original research articles on related topics.

Previously published in the Journal of Elasticity, Volume 119, Issue 1-2, 2015.

Editors and Affiliations

  • Aeropsace Engineering and Mechanics, University of Minnesota, Minneapolis, USA

    Roger Fosdick

  • Okinawa Institute of Science and Technol Mathematical Soft Matter Unit, Okinawa, Japan

    Eliot Fried

Bibliographic Information

  • Book Title: The Mechanics of Ribbons and Möbius Bands

  • Editors: Roger Fosdick, Eliot Fried

  • DOI: https://doi.org/10.1007/978-94-017-7300-3

  • Publisher: Springer Dordrecht

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing Switzerland 2016

  • Hardcover ISBN: 978-94-017-7299-0Published: 27 August 2015

  • Softcover ISBN: 978-94-024-0213-1Published: 23 August 2016

  • eBook ISBN: 978-94-017-7300-3Published: 14 August 2015

  • Edition Number: 1

  • Number of Pages: VI, 352

  • Number of Illustrations: 26 b/w illustrations, 86 illustrations in colour

  • Topics: Solid Mechanics, Computational Science and Engineering, Biological and Medical Physics, Biophysics, Nanotechnology

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