Buckling cascade of free-standing mesoscopic beams

We have observed a striking change in the static equilibrium shape of freestanding mesoscopic buckled beams as a function of the length-to-width aspect ratio. At low values of the aspect ratio the shape is well described by classical Euler buckling. At higher values the buckled shapes become more complex and are well described by a superposition of buckling modes. The data are consistent with a mode-coefficient sum rule obtained from a nonlinear elastic field theory. Further, for beams of low aspect ratio the theory can predict the equilibrium shape of the buckling, while at high aspect ratios the lower bound on the buckling shape function is obtained.