The Mechanics of Self-Folding Structures

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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.