Mapping of Fold Path Bifurcations in Origami Structures

Origami has proven value in numerous technological applications including lightweight composites, soft robotics, metamaterial design, and deployable space structures, where discrete and modular folding motifs are leveraged to form novel tessellations. The material (stiffness mismatch among deformation modes) and geometric (slender elements) contrasts in origami structures can lead to highly nonlinear mechanical behavior with unique macroscopic properties, such as multi-stability. To efficiently navigate this complex nonlinear space, we have recently developed an efficient nonlinear truss finite element model with linear eigenanalysis heuristics for branch switching off the flat state. However, more efficient and robust methods have proven essential when performing topology optimization in this non-convex design space involving energy landscapes with many bifurcations and stable equilibrium points. Our work focuses on the incorporation of robust continuation methods for bifurcation point detection and branch switching to map these multistable energy landscapes and characterize the role of discrete fold stiffness distributions.