Pattern Transitions in a Soft Cylindrical Shell

TL;DR

This study investigates pattern transitions in a soft cylindrical shell under compression, revealing a complex sequence of buckling phenomena including wrinkles, ridges, and sagging, driven by curvature effects and characterized by bifurcations and hysteresis.

Contribution

It uncovers a novel sequence of pattern transitions in soft shells on curved surfaces, demonstrating the generality of bifurcation phenomena independent of material models.

Findings

Identification of smooth-wrinkle-ridge-sagging transitions

Observation of hysteresis loops and co-existing patterns

Demonstration of bifurcation scheme's generality

Abstract

Instability patterns of rolling up a sleeve appear more intricate than the ones of walking over a rug on floor, both characterized as uniaxially compressed soft-film/stiff-substrate systems. This can be explained by curvature effects. To investigate pattern transitions on a curved surface, we study a soft shell sliding on a rigid cylinder by experiments, computations and theoretical analyses. We reveal a novel post-buckling phenomenon involving multiple successive bifurcations: smooth-wrinkle-ridge-sagging transitions. The shell initially buckles into periodic axisymmetric wrinkles at the threshold and then a wrinkle-to-ridge transition occurs upon further axial compression. When the load increases to the third bifurcation, the amplitude of the ridge reaches its limit and the symmetry is broken with the ridge sagging into a recumbent fold. It is identified that hysteresis loops and the Maxwell equal-energy conditions are associated with the co-existence of wrinkle/ridge or ridge/sagging patterns. Such a bifurcation scheme is inherently general and independent of material constitutive models.