Powering the Renaissance: Methods to Reveal the Energy Landscapes in Thin Shell Buckling

The extreme non-linearity of thin shell buckling introduces significant challenges to studying even the simplest geometries. Here, we develop a new approach by coupling efficient and powerful energy landscape methods to a conceptually simple discretized elastic mesh model. This highly versatile approach can probe the buckling energy landscape of any thin shell, or composite of thin shells, without the need for a priori assumptions about deformation morphologies or symmetries.

As an example, we investigate the landscape of an axially compressed cylinder, revealed to be remarkably rich and highly variable as a function of aspect ratio and compressive strain. Firstly, we observe that a relatively small, discrete set of sub-critical buckled states balloons in size as the aspect ratio is increased. We then use a string method to obtain the minimum energy pathways between any two minima. We show how experimental local probing techniques can access the true initial buckling transition for centrally-located dimples. By recursively connecting the local minima, we reveal the landscape to be dominated by a small number of multiply-dimpled states at small aspect ratios, becoming glassy and highly-connected at large aspect ratios, and featuring many multi-step pathways between minimum pairs.