  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.
