Geometric Mechanics of Cellular Origami Assemblages

折纸启发的结构可以有从人造材料和微型机器人到可部署的太阳能电池阵列和建筑立面的应用范围。这些系统可以通过折叠薄板或用柔性铰链连接薄板来创建。折纸吸引了实际应用，因为它可以紧凑地存放，并且可以部署到可变形的移动结构中。这种可展开的组合体可以极大地增强薄板系统的特性和潜在应用。关于这些结构仍有许多未知之处。 这项研究的首要目标是创建数学模型和物理原型，捕捉薄片的行为（线性和非线性，包括不稳定性），并使用这些来探索管状和细胞折纸组装的力学。这项转化研究将通过整合活性材料、设计理论、数学（几何折纸）和艺术表达，为在工程中使用薄板组装提供一个新的范例。这些系统可以为空间探索（例如可展开结构）、机器人（例如机械臂）、医学（例如支架）和其他研究领域提供解决方案。跨学科的方法将有助于扩大代表性不足的群体参与研究，并通过使用折纸作为整合不同学科知识的手段，对工程教育产生积极影响。计算机代码和折纸的几何变化将在开源平台上发布，大大扩展了折纸的实际应用。这项研究的智力价值在于理解折纸组装的几何变化和弹性特性，非线性力学，以及包括双稳态-多稳态配置的不稳定性。该研究将探索刚性可折叠折纸管和装配的几何变化，创建分析模型来模拟薄片折纸系统的非线性，并捕获可变形/可重构折纸结构的不稳定性。它将研究新颖的折纸组合，如那些弯曲的轮廓，多边形横截面（N-线），或多个管耦合在一起。本研究将归纳不同组合体的几何定义，并研究每个系统的运动学、本征模态变形和材料行为。由于薄片组装是有用的超出小位移的假设，研究将探讨大位移和相关的折纸非线性行为。将建立新的计算机模型，它可以捕捉到与薄板系统相关的各种非线性。一个统一的迭代方案将被用来研究折纸，证明要么接近零或负刚度。这些不稳定性的能量状态将为可变形折纸的实际应用提供信息。当科学家和工程师使用不同尺度的薄片折纸系统时，机械性能将是有用的。

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.