Influence of material stretchability on the equilibrium shape of a Mobius band

DM Kleiman and DF Hinz and Y Takato and E Fried, SOFT MATTER, 12, 3750-3759 (2016).

DOI: 10.1039/c5sm02188j

We use a two-dimensional discrete, lattice-based model to show that Mobius 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 Mobius 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 Mobius bands from materials with continuum parameters that can be measured experimentally or estimated by upscale averaging.

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