Interplay of gross and fine morphologies of unstretchable balloons

From high-altitude balloons to candy wrappers, planar sheets of thin films are commonly forced into doubly bent shapes. A key challenge is to understand the overall gross shape that is selected, and how it constrains the fine features, such as wrinkles, crumples, or creases. Here, we study a thin-membraned balloon as a prototypical system that involves a doubly curved gross shape with large amplitude undulations. By probing its profiles and cross sections, we discover that an existing geometric model developed for a film with small-scale wrinkles can capture the mean behavior of the film, even when the wrinkle amplitude is large. We then propose a minimal model for a representative balloon cross-section, as an elastic filament subjected to an effective pinning potential around the mean shape. Our parsimonious model reproduces a broad range of phenomena seen in the experiments, from morphological changes with pressure to the detailed shape of the wrinkles and folds. Our results establish a new route to analyzing finite buckled structures over an enclosed surface, which could aid the design of inflatable structures.