The crepe problem: folding, rolling, and stability of heavy elastic sheets.

Folding and rolling are universal strategies for compactly storing, deploying, or encapsulating materials. In this study, we explore the smooth loops and rolls that emerge when elastic sheets are folded, focusing on scenarios where gravity competes with bending stiffness. Through a combination of experiments, geometric analysis, and elasticity theory, we identify a characteristic elasto-gravity length that governs both the shape and stability of these folds. We map the transition from stable to unstable configurations and quantify the role of friction in shifting these boundaries. Extending our analysis to systems with multiple folds, we derive scaling laws for stacking and demonstrate how rolled configurations can encapsulate or even transport objects. Our findings offer a unified, geometry-driven framework for understanding folding and rolling in soft materials, revealing how weight, bending, and friction interact to shape and mobilize thin elastic sheets. These insights provide simple, robust design principles for deployable soft structures and efficient packaging systems.