  A growing or compressed thin elastic sheet adhered to a rigid substrate can
exhibit a buckling instability, forming an inward hump. Our study shows that
the strip morphology depends on the delicate balance between the compression
energy and the bending energy. We find that this instability is a first order
phase transition between the adhered solution and the buckled solution whose
main control parameter is related to the sheet stretchability. In the nearly-
unstretchable regime we provide an analytic expression for the critical
threshold. Compressibility is the key assumption which allows us to resolve the
apparent paradox of an unbounded pressure exerted on the external wall by a
confined flexible loop.
