Equilibrium shapes with stress localisation for inextensible elastic möbius and other strips

Book chapter


Starostin, EL and Van Der Heijden, GHM (2016). Equilibrium shapes with stress localisation for inextensible elastic möbius and other strips. in: The Mechanics of Ribbons and Möbius Bands pp. 67-112
AuthorsStarostin, EL and Van Der Heijden, GHM
Abstract

© Springer Science+Business Media Dordrecht 2015. We formulate the problem of finding equilibrium shapes of a thin inextensible elastic strip, developing further our previous work on the Möbius strip. By using the isometric nature of the deformation we reduce the variational problem to a second-order onedimensional problem posed on the centreline of the strip. We derive Euler-Lagrange equations for this problem in Euler-Poincaré form and formulate boundary-value problems for closed symmetric one-and two-sided strips. Numerical solutions for the Möbius strip show a singular point of stress localisation on the edge of the strip, a generic response of inextensible elastic sheets under torsional strain. By cutting and pasting operations on the Möbius strip solution, followed by parameter continuation, we construct equilibrium solutions for strips with different linking numbers and with multiple points of stress localisation. Solutions reveal how strips fold into planar or self-contacting shapes as the length-to-width ratio of the strip is decreased. Our results may be relevant for curvature effects on physical properties of extremely thin two-dimensional structures as for instance produced in nanostructured origami.

Page range67-112
Year2016
Book titleThe Mechanics of Ribbons and Möbius Bands
ISBN9789401772990
Publication dates
Print01 Jan 2016
Publication process dates
Deposited14 Jan 2020
Digital Object Identifier (DOI)doi:https://www.doi.org/10.1007/978-94-017-7300-3
Accepted author manuscript
License
CC BY 4.0
File Access Level
Open
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https://openresearch.lsbu.ac.uk/item/88w83

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