Two instabilities underlying curvature-induced delamination patterns

We adderess the delamination of a thin solid film from an adhesive, spherically-shaped substrate. Scaling arguments suggest that delamination may occur through two distinct instabilities. The first is local -- triggered solely by a compressive, curvature-induced component of the film stress. This instability is akin to the delamination of a uniaxially-compressed film from a flat substrate, and is thus reminiscent of Euler buckling and wrinkling instabilities, hence we refer to it as ``Euler-like". The second instability occurs when the total strain energy, associated with both tensile and compressive components of the stress and integrated over the film, reaches a a separate threshold. We refer to this instability as ``Gauss-like".
We argue that the Gauss-like instability, which has been considered previously as the building block of curvature-induced blister networks, dominates for moderately bendable films. In contrast, the Euler-like instability, whose role for curvature-induced delamination has not been noted so far, governs the mechanics of highly bendable films and gives rise to patterns of elongated, radially-oriented folds or rucks. We present experimental results that support the existence of distinct instability mechanisms for curvature-induced delamination.