title: Influence of material stretchability on the equilibrium shape of a Möbius band.
abstract: We use a two-dimensional discrete, lattice-based model to show that Möbius bands made with stretchable materials are less likely to crease or tear. This stems from a delocalization of twisting strain that occurs if stretching is allowed. The associated low-energy configurations provide strategic target shapes for the guided assembly of nanometer and micron scale Möbius bands. To predict macroscopic band shapes for a given material, we establish a connection between stretchability and relevant continuum moduli, leading to insight regarding the practical feasibility of synthesizing Möbius bands from materials with continuum parameters that can be measured experimentally or estimated by upscale averaging.
authors.affiliation: Department of Mathematics and Statistics, McGill University, Montréal, Québec, Canada H3A 2K6. dave.kleiman2@gmail.com.
authors.forename: David M
authors.initials: DM
authors.lastname: Kleiman
authors.affiliation: Kamstrup A/S, Industrivej 28, Stilling, 8660 Skanderborg, Denmark. dfhinz@gmail.com.
authors.forename: Denis F
authors.initials: DF
authors.lastname: Hinz
authors.affiliation: Mathematical Soft Matter Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa, Japan 904-0495. yoichi.takato@oist.jp eliot.fried@oist.jp.
authors.forename: Yoichi
authors.initials: Y
authors.lastname: Takato
authors.affiliation: Mathematical Soft Matter Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa, Japan 904-0495. yoichi.takato@oist.jp eliot.fried@oist.jp.
authors.forename: Eliot
authors.initials: E
authors.lastname: Fried