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The Mechanics of Self-Folding Structures

自折叠结构的力学

基本信息

批准号：
2217543
负责人：
Christian Santangelo
金额：
$ 29.84万
依托单位：
Syracuse University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-04-01 至 2024-02-29
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2217543&HistoricalAwards=false
关键词：
Mechanics Self Folding Structures

项目摘要

Nontechnical Summary This award supports theoretical and computational research, and education on mechanical structures that are made from programmable and responsive materials, and fold themselves into 3D shapes from an initially flat shape. Self-folding material structures are poised to revolutionize manufacturing, particularly by allowing the fabrication of very complex three-dimensional structures from sizes less than a millimeter to human scale. Because they are fabricated flat, self-folding structures can be made cheaply, rapidly, and in bulk. However, one of the primary obstacles to realizing this technology is the proliferation of misfolded structures. The PI and his team will develop new theoretical and computation tools to design material structures that will fold robustly, thus removing this manufacturing obstacle. The research will also establish connections between the mechanics of self-folding materials structures and the mechanics of material shells more generally by incorporated tools from the field of discrete geometry. This project will introduce graduate students to cutting edge techniques in the analysis of materials, and foster collaborations between theory and experiment. The methods developed in this project will be incorporated into a computational package that will be documented and distributed to the broader materials community. An educational module on geometry and origami for middle school will be developed to introduce students to mathematical thinking. Technical Summary This award supports theoretical and computational research, and education on self-folding origami structures. Self-folding origami structures are poised to revolutionize manufacturing by providing an easy means of creating complex three-dimensional geometries from an initially flat substrate on any length scale. Recently, there has been a great deal of effort devoted to creating material systems that can be fabricated to fold or unfold upon application of an external stimulus. While many complex folding structures fold robustly into their target shape, many do not, even when the fold patterns are simple. One of the primary obstacles to realizing such structures is the bifurcated nature of the configuration space, which exhibits a multitude of branches that are exponential in the complexity of the structure. This is a key and unavoidable feature of the way such structures deform and leads to apparent glass-like behavior in folding. The PI will develop a theory for the mechanics of self-folding structures and devise principles by which those structures can be made to fold robustly. The scientific aims of this project, specifically, are to develop a theory for the configuration space of self-folding structures that incorporates the bending elasticity of folds, allows for the introduction of Gaussian curvature at vertices, and properly accounts for the geometrical rigidity of the structures at second-order and beyond. This project will have an impact on the design of structured materials by introducing new analytical techniques for the prediction of three-dimensional structures. It will lead to the further development and documentation of a software package in Mathematica that can be used to perform complex calculations on rigid mechanisms. It also funds a number of education activities, including the training of a graduate student in cutting edge theoretical techniques. An educational module on geometry and origami for middle school will be developed to introduce students to mathematical thinking.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项支持理论和计算研究，以及由可编程和响应材料制成的机械结构的教育，并从最初的平面形状折叠成3D形状。自折叠材料结构有望彻底改变制造业，特别是通过允许制造非常复杂的三维结构，从小于一毫米的尺寸到人类尺度。因为它们是扁平的，自折叠结构可以便宜、快速、批量地制造。然而，实现该技术的主要障碍之一是错误折叠结构的扩散。PI和他的团队将开发新的理论和计算工具，以设计能够牢固折叠的材料结构，从而消除这种制造障碍。该研究还将建立自折叠材料结构力学和材料壳力学之间的联系，更一般地通过离散几何领域的整合工具。这个项目将向研究生介绍材料分析的尖端技术，并促进理论和实验之间的合作。在这个项目中开发的方法将被纳入一个计算包，将被记录和分发给更广泛的材料社区。将开发一个中学几何和折纸教育模块，向学生介绍数学思维。该奖项支持自折叠折纸结构的理论和计算研究以及教育。自折叠折纸结构准备通过提供从任何长度尺度上的初始平坦衬底创建复杂三维几何形状的简单手段来彻底改变制造。最近，已经有大量的努力致力于创造材料系统，该材料系统可以被制造成在施加外部刺激时折叠或展开。虽然许多复杂的折叠结构能稳健地折叠成它们的目标形状，但许多结构不能，即使折叠模式很简单。实现这样的结构的主要障碍之一是配置空间的分叉性质，其表现出在结构的复杂性中呈指数的多个分支。这是这种结构变形方式的一个关键和不可避免的特征，并导致折叠时明显的玻璃状行为。PI将开发自折叠结构的力学理论，并设计这些结构可以稳健折叠的原理。具体来说，该项目的科学目标是开发一种自折叠结构配置空间的理论，该理论结合了折叠的弯曲弹性，允许在顶点引入高斯曲率，并适当地解释了结构的几何刚性。二阶及以上。该项目将通过引入用于预测三维结构的新分析技术对结构材料的设计产生影响。这将导致进一步开发和文档的Mathematica软件包，可用于执行复杂的计算刚性机制。它还资助一些教育活动，包括培训一名研究生掌握尖端理论技术。该奖项反映了NSF的法定使命，通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。