  Everyday experience confirms the tendency of adhesive films to detach from
spheroidal regions of rigid substrates -- what is a petty frustration when
placing a sticky bandage onto an elbow or knee is a more serious matter in the
coating and painting industries. Irrespective of their resistance to bending, a
key driver of such phenomena is Gauss' \textit{Theorema Egregium}, which
implies that naturally flat sheets cannot conform to doubly-curved surfaces
without developing a strain whose magnitude grows sharply with the curved area.
Previous attempts to characterize the onset of curvature-induced delamination,
and the complex patterns it gives rise to, assumed a dewetting-like mechanism
in which the propensity of two materials to form contact through interfacial
energy is modified by an elastic energy penalty. We show that this approach may
characterize moderately bendable adhesive sheets, but fails qualitatively to
describe the curvature-induced delamination of ultrathin films, whose mechanics
is governed by their propensity to buckle under minute levels of compression.
Combining mechanical and geometrical considerations, we introduce a minimal
model for curvature-induced delamination that accounts for two elementary
buckling motifs, shallow "rucks" and localized "folds". We predict nontrivial
scaling rules for the onset of curvature-induced delamination and various
features of the emerging patterns, which compare well with experimental
observations. Beyond gaining control on the use of ultrathin adhesives in
cutting edge technologies such as stretchable electronics, our analysis is a
significant step towards quantifying the multiscale morphological complexity
that emerges upon imposing geometrical and mechanical constraints on highly
bendable solid objects.
