Kinetic wavelength selection in an unsupported annulus contracted radially at the inner boundary

The prototypical system for studying two-dimensional (2d) wrinkling is the Lamé system – a thin annulus subjected to radial tensile loads at both boundaries so that the material circles wrinkle. The number of wrinkles (i.e. wavenumber) depends on the applied tensile loading or the presence of an external substrate. In [1], we analyse a novel Lamé system: an unsupported annulus that is pulled in only at the inner boundary, and buckles into a radially wrinkled configuration that is developable and hence strain-free. But what sets the system wavelength in the absence of a substrate or tension field? Here, we propose a kinetic mechanism in which the wavelength is set by a combination of dynamic wrinkling wavelengths [2], and wavelength coarsening features called ‘wrinklons’ [3]. We support our claims using finite-element simulations.

References –

[1] Pal, Pocivavsek, Witten (unpublished)

[2] Box et al, PRL 2020

[3] Vandeparre et al, PRL 2011