Semiflexible origami and their many minima*

Self-folding origami structures, which allow flat materials to be deployed into three dimensional structures, have many engineering applications. These applications, however, require that the structures fold without error and robustly. For infinitely rigid origami, many configuration space components meet at the flat, unfolded state, so even when every fold is programmed to the desired equilibrium result, the structure can misfold into an undesired branch of configurations. Here, we show how to relax the rigidity of origami by allowing a small amount of stretching along the folds, which in turn allows Gaussian curvature at the vertices. We map the energy landscape for simple origami and explore the bifurcations of the energy landscape that lead to multiple minima. Furthermore, we explore how the basins of attraction of different energy minima affect the potential to misfold.