Geometrically-frustrated wrinkle patterns 2: cascades versus defects

Cascades and localized defects are characteristic motifs of wrinkle patterns in
elastic sheets, appearing when a array of uniformly-spaced wrinkled is incom-
patible with a confining topography, boundary conditions, or gradients in the
sheet’s thickness or the stiffness of a supporting substrate. Inspired by a recent
experimental study (J. Schleifer et al. Soft Matter 15 1405 (2019)), we employ
numerical simulations to study the wrinkle patterns in a uniaxially-compressed
sheet, floating on a liquid bath whose density in non-uniform, implying a gra-
dient in the locally-favored value of the wrinkle wavelength in the direction
orthogonal to the axis of compression. This simple model enables a systematic
study of the basic mechanisms through which the wrinkle density and wave-
length vary in space. Exploring the parameter regimes that correspond to weak
and strong gradient of the liquid density, we show that the meso-scale features
of the pattern may be determined by distinct physical mechanisms that involve
cascade-like structures and localized defects