Dynamics of the Euler Buckling Instability

ABSTRACTWe review recent systematic investigations of the dynamics of the classical Euler buckling of compressed solid membranes and thin sheets. We relate the membrane buckling dynamics to phase ordering phenomena. Evolving membranes develop wavelike patterns whose wavelength grows, via coarsening, as a power of time. We find that evolving membranes are similar to interfaces of thin films in molecular-beam epitaxy growth with slope selection: They are characterized by the presence of mounds whose typical size grows as a power of time. The morphologies of the evolving membranes are characterized by the presence of a network of growing ridges where the elastic energy is mostly concentrated. We used this fact to develop a scaling theory of the buckling dynamics that gives analytic estimates of the coarsening exponents. Our findings show that the membrane buckling dynamics is characterized by a distinct scaling behavior not found in other coarsening phenomena.