The Mechanics of Ribbons and Möbius Bands

by Roger Fosdick, Eliot Fried

Overview

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.

Product Details

ISBN-13:	9789402402131
Publisher:	Springer Netherlands
Publication date:	08/23/2016
Edition description:	Softcover reprint of the original 1st ed. 2016
Pages:	352
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

Foreword.- 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.- Translation and Interpretation of Michael Sadowsky’s Paper “Theory of Elastically Bendable Inextensible Bands with Applications to Möbius Band”.- Translation of Michael Sadowsky’s Paper “The Differential Equations of the Möbius Band”.- Translation of W. Wunderlich’s “On a Developable Möbius Band.- Gamma-Limit of a Model for the Elastic Energy of an Inextensible Ribbon.- “Wunderlich, Meet Kirchhoff”: A General and Unified Description of Elastic Ribbons and Thin Rods.- Equilibrium Shapes with Stress Localisation for Inextensible Elastic Möbius and Other Strips.- Bending Paper and the Möbius Strip.- Roadmap to the Morphological Instabilities of a Stretched Twisted Ribbon.- The Shrinking Figure Eight and Other Solitons for the Curve Diffusion Flow.- Kinematical Aspects of Levi-Civita Transport of Vectors and Tensors Along a Surface Curve.- Non-Euclidean Ribbons.- The Second-Order L 2 Flow of Inextensible Elastic Curves with Hinged Ends in the Plane.- Buckling of Naturally Curved Elastic Strips: The Ribbon Model Makes a Difference.- Residual Stresses and Poisson’s Effect Drive Shape Formation and Transition of Helical Structures.- Representation for a Smooth Isometric Mapping from a Connected Planar Domain to a Surface.