Asymptotic isometry and wrinkle-to-fold transition in a simplified Lamé problem

Azimuthal wrinkling in the annular (Lamé) geometry serves as an archetype for understanding geometry-influenced elastic response in thin sheets. In most experiments, the annulus is subjected to radial tension at both the inner and outer boundaries, generating compression and wrinkling in the azimuthal direction ([1]) . In our work, we study an even simpler version of this problem, using theory and simulations, where the annulus is subjected to only a radial pull at the inner boundary. This creates azimuthal wrinkling with a simpler, one-dimensional phase space spanned by the dimensionless 'bendability' parameter, ε^-1.We focus on the large ε^-1(small thickness and/or large load) limit -- here, in contrast to previous experiments, the sheet becomes asymptotically isometric, and the wavenumber coarsens and hits a lower limit set by the geometry of the sheet and the boundary conditions. If we now loosen the boundary condition, the wrinkles transition to a single fold that consumes all the excess length. Although purely numerical, to the best of our knowledge, this is the first realisation of a wrinkle-to-fold transition ([2]) on an unsupported membrane.

References -
1. Davidovitch et al, PNAS 2011
2. Brau et al, Soft Matter 2013