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