Buckling cascade of thin plates: Forms, constraints and similarity

We experimentally study compression of thin plates in rectangular boxes with variable height. A cascade of buckling is generated. It gives rise to a self-similar evolution of elastic reaction of plates with box height which surprisingly exhibits repetitive vanishing and negative stiffness. These features are understood from properties of Euler’s equation for elastica. Elastic thin plates submitted to a sufficiently large in-plane load are well-known to spontaneously bend due to buckling instability [1]. However, this phenomenon, which is often quoted as a canonical example of primary bifurcation in out-of-equilibrium systems, has been little investigated in the fully non-linear regime [2, 3, 4, 5, 6]. Yet, it provides an appealing opportunity of yielding pattern formations within a non-local variational framework- elasticity- free of significant noise disturbances. In addition, it plays an essential role in the mechanical resistance of homogenous or layered materials and involves important practical implications regarding packaging, safety structures or in-load behaviour of plywood or film-substrate composites. Therefore, for both fundamental and practical reasons, the non-linear buckling regime of thin plates warrants a renewal of interest from physicists. This Letter is devoted to experimentally studying buckling of thin plates from the quasi-linear