Nonlinear Mechanics of Origami’s Critical Point: Understanding and Designing around Flat State Transitions

Origami, the art of paper folding, has proven to be a transformative technology in science and engineering with applications including structural composites, electromagnetic devices, mechanical metamaterials, and space deployable structures. The large localized rotations and stiffness mismatch between folding and facet stretching/bending creates a highly nonlinear structure that exhibits unique properties, such as multi-stability and/or auxetic behavior. However, navigating the origami design space is challenging due to branching and limited energetic discrimination between possible fold paths. To investigate the challenge, we combine a nonlinear truss model and topology optimization techniques to identify methods of robust fold path selection. We focus on design of multistable origami structures with multiple internal vertices, and introduce techniques for exploring critical points and bifurcations (which often occur during a flat state transition). Objective functions are explored where these bifurcations are avoided or encouraged in addition to design of the overall energy landscape (location and number of equilibrium points). This analysis and design framework allows for generic tuning of the equilibrium states of the structure to achieve application specific performance.