Geometric Mechanics of Cellular Origami Assemblages

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Origami inspired structures can have applications ranging in scale from man-made materials and micro-robotics to deployable solar arrays and building facades. These systems can be created by creasing a thin sheet or connecting thin panels with flexible hinges. Origami appeals for practical applications because it can be stowed compactly and it can be deployed into a transformable moving structure. Such deployable assemblages can drastically enhance the characteristics and potential applications of the thin sheet system. Much remains unknown about these configurations. The overarching goal of this research is to create mathematical models and physical prototypes that capture the behavior (both linear and nonlinear, including instability) of thin sheets, and to use these to explore the mechanics of tubular and cellular origami assemblages. This translational research will provide a new paradigm for using thin sheet assemblages in engineering through the integration of active materials, design theory, mathematics (geometric origami), and artistic expression. These systems may provide solutions for space exploration (e.g. deployable structures), robotics (e.g. robotic arms), medicine (e.g. stents), and other fields of study. The interdisciplinary approach will help broaden participation of underrepresented groups in research and positively impact engineering education by using origami as a means to integrate knowledge in different disciplines. The computer codes and geometric origami variations will be distributed in open-source platforms, greatly extending the practical applications of origami.The intellectual merit of this research lies in understanding origami assemblages for their geometric variations and elastic properties, nonlinear mechanics, and instabilities including bistable-multistable configurations. The research will explore geometric variations of rigid foldable origami tubes and assemblages, create analytical models to simulate nonlinearities in thin sheet origami systems, and capture instability in transformable/reconfigurable origami structures. It will study novel origami assemblages such as those with curved profiles, polygonal cross-sections (N-gons), or multiple tubes coupled together. The research will generalize the geometric definitions for different assemblages, and study the kinematics, eigen-mode deformations, and material behavior of each system. Because thin sheet assemblages are useful beyond the assumptions of small displacements, the research will explore large displacements and the associated nonlinear behavior of origami. New computer models will be established, which can capture various nonlinearities associated with the thin sheet systems. A unified iterative scheme will be used to study origami that demonstrates either near-zero or negative stiffness. The energy states of these instabilities will inform practical applications of the transformable origami. The mechanical properties will be useful to scientist and engineers when using thin sheet origami systems of varying scales.