Inspired by the allure of additive fabrication, we pose the problem of origami design from a different perspective: How can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable fourfold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets. We illustrate the flexibility of our approach by growing ordered, disordered, straight, and curved-folded origami and fitting surfaces of given curvature with folded approximants. Overall, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based metastructure design.
Several strategies are recently exploited to transform 2D sheets into desired 3D structures. For example, soft materials can be morphed into 3D continuously curved structures by inducing nonhomogeneous strain. On the other hand, rigid materials can be folded, often by origami/kirigami‐inspired approaches (i.e., flat sheets are folded along predesigned crease patterns). Here, for the first time, combining the two strategies, composite sheets are fabricated by embedding rigid origami/kirigami skeleton with creases into heat shrinkable polymer sheets to create novel 3D structures. Upon heating, shrinkage of the polymer sheets is constrained by the origami/kirigami patterns, giving rise to laterally nonuniform strain. As a result, Gaussian curvature of the composite sheets is changed, and flat sheets are transformed into 3D curved structures. A series of 3D structures are folded using this approach, including cones and truncated pyramids with different base shapes. Flat origami loops are folded into step structures. Tessellation of origami loops is transformed into 3D checkerboard pattern.
more » « less- NSF-PAR ID:
- 10066744
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Advanced Functional Materials
- Volume:
- 28
- Issue:
- 44
- ISSN:
- 1616-301X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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