The Mechanics of Ribbons and Möbius Bands

Front Matter....Pages I-VI
Foreword....Pages 1-2
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”....Pages 3-6
Translation and Interpretation of Michael Sadowsky’s Paper “Theory of Elastically Bendable Inextensible Bands with Applications to the Möbius Band”....Pages 7-17
Translation of Michael Sadowsky’s Paper “The Differential Equations of the Möbius Band”....Pages 19-22
Translation of W. Wunderlich’s “On a Developable Möbius Band”....Pages 23-34
Gamma-Limit of a Model for the Elastic Energy of an Inextensible Ribbon....Pages 35-47
“Wunderlich, Meet Kirchhoff”: A General and Unified Description of Elastic Ribbons and Thin Rods....Pages 49-66
Equilibrium Shapes with Stress Localisation for Inextensible Elastic Möbius and Other Strips....Pages 67-112
Bending Paper and the Möbius Strip....Pages 113-136
Roadmap to the Morphological Instabilities of a Stretched Twisted Ribbon....Pages 137-189
The Shrinking Figure Eight and Other Solitons for the Curve Diffusion Flow....Pages 191-211
Kinematical Aspects of Levi-Civita Transport of Vectors and Tensors Along a Surface Curve....Pages 213-249
Non-Euclidean Ribbons....Pages 251-261
The Second-Order  \(L^{2}\) -Flow of Inextensible Elastic Curves with Hinged Ends in the Plane....Pages 263-291
Buckling of Naturally Curved Elastic Strips: The Ribbon Model Makes a Difference....Pages 293-320
Residual Stresses and Poisson’s Effect Drive Shape Formation and Transition of Helical Structures....Pages 321-333
Representation for a Smooth Isometric Mapping from a Connected Planar Domain to a Surface....Pages 335-350
Erratum to: Four Papers Published in the Journal of Elasticity (2015) 119(1–2)....Pages 351-352