The Mechanics of Ribbons and Möbius Bands

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.

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

Inhalt

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.