Bifurcation of pre-buckled bands under lateral transverse shear*

We combine experiments and simulations to study the supercritical pitchfork bifurcation of a pre-compressed band under lateral end translation, from narrow to wide. Based on the ratio among length, width, and thickness, the elastic structures in our study fall into three different categories: rods, ribbons, and plates. To capture their geometrically nonlinear deformations, we develop several discrete differential geometry-based numerical frameworks. The one dimensional rod model can predict the mechanical response when the plate is narrow, while it is unable to match with experiments as the width of the band increases. A two dimensional approach (plate model) can accurately predict the deformations of bands with different geometries. The ribbon model of Sadowsky, surprisingly, fails to capture the mechanics of strips at inflection points. Our study provides guidelines on the choice of the appropriate models – rod, ribbon, and plate – in simulation of slender structures.