We consider the behavior of buckling driven thin-film blisterings using von
Karman's plate theory. Our focus is on the setting where the blistered reg
ion is the unit square with clamped boundary conditions at the vertical sid
es and periodic ones along the horizontal sides. In this setting, we prove
rigorous upper and lower bounds for the elastic energy which are of the sam
e order as the film thickness. We also present a convincing argument for th
e necessity of branching of folds near the boundary as has been observed in
experiments. (C) 2001 American Institute of Physics.