Curvature-Driven Wrinkling of Thin Elastic Shells

How much energy does it take to stamp a thin elastic shell flat? Motivated by recent experiments on the wrinkling patterns of floating shells, we develop rigorous method via $\Gamma$-convergence for answering this question leading order in shell's thickness and other small parameters. The observed involve "ordered" regions well-defined wrinkles alongside "disordered" whose local features are less robust; as little no tension is applied, preference not priori clear. Rescaling typical pattern, derive limiting variational problem effective displacement shell. It asks, linearized way, cover up maximum area with length-shortening map plane. Convex analysis yields boundary value characterizing accompanying their defect measures. Partial uniqueness regularity theorems follow from characteristics ordered part In can deduce principle minimum stamped shells.