Continuum Field Theory for the Deformations of Planar Kirigami.

Mechanical metamaterials exhibit exotic properties that emerge from the interactions of many nearly rigid building blocks. Determining these properties theoretically has remained an open challenge outside a few select examples. Here, for a large class of periodic and planar kirigami, we provide a coarse-graining rule linking the design of the panels and slits to the kirigami's macroscale deformations. The procedure gives a system of nonlinear partial differential equations expressing geometric compatibility of angle functions related to the motion of individual slits. Leveraging known solutions of the partial differential equations, we present an illuminating agreement between theory and experiment across kirigami designs. The results reveal a dichotomy of designs that deform with persistent versus decaying slit actuation, which we explain using the Poisson's ratio of the unit cell.

Origami-inspired thin-film shape memory alloy devices.

We describe the design and fabrication of miniaturized origami structures based on thin-film shape memory alloys. These devices are attractive for medical implants, as they overcome the opposing requirements of crimping the implant for insertion into an artery while keeping sensitive parts of the implant nearly stress-free. The designs are based on a group theory approach in which compatibility at a few creases implies the foldability of the whole structure. Importantly, this approach is versatile and thus provides a pathway for patient-specific treatment of brain aneurysms of differing shapes and sizes. The wafer-based monolithic fabrication method demonstrated here, which comprises thin-film deposition, lithography, and etching using sacrificial layers, is a prerequisite for any integrated self-folding mechanism or sensors and will revolutionize the availability of miniaturized implants, allowing for new and safer medical treatments.

Helical Miura origami.

We characterize the phase space of all helical Miura origami. These structures are obtained by taking a partially folded Miura parallelogram as the unit cell, applying a generic helical or rod group to the cell, and characterizing all the parameters that lead to a globally compatible origami structure. When such compatibility is achieved, the result is cylindrical-type origami that can be manufactured from a suitably designed flat tessellation and "rolled up" by a rigidly foldable motion into a cylinder. We find that the closed helical Miura origami are generically rigid to deformations that preserve cylindrical symmetry but are multistable. We are inspired by the ways atomic structures deform to develop two broad strategies for reconfigurability: motion by slip, which involves relaxing the closure condition, and motion by phase transformation, which exploits multistability. Taken together, these results provide a comprehensive description of the phase space of cylindrical origami, as well as quantitative design guidance for their use as actuators or metamaterials that exploit twist, axial extension, radial expansion, and symmetry.

Patterning nonisometric origami in nematic elastomer sheets.

Nematic elastomers dramatically change their shape in response to diverse stimuli including light and heat. In this paper, we provide a systematic framework for the design of complex three dimensional shapes through the actuation of heterogeneously patterned nematic elastomer sheets. These sheets are composed of nonisometric origami building blocks which, when appropriately linked together, can actuate into a diverse array of three dimensional faceted shapes. We demonstrate both theoretically and experimentally that the nonisometric origami building blocks actuate in the predicted manner, and that the integration of multiple building blocks leads to complex, yet predictable and robust, shapes. We then show that this experimentally realized functionality enables a rich design landscape for actuation using nematic elastomers. We highlight this landscape through examples, which utilize large arrays of these building blocks to realize a desired three dimensional origami shape. In combination, these results amount to an engineering design principle, which provides a template for the programming of arbitrarily complex three dimensional shapes on demand.

Programming complex shapes in thin nematic elastomer and glass sheets.

Nematic elastomers and glasses are solids that display spontaneous distortion under external stimuli. Recent advances in the synthesis of sheets with controlled heterogeneities have enabled their actuation into nontrivial shapes with unprecedented energy density. Thus, these have emerged as powerful candidates for soft actuators. To further this potential, we introduce the key metric constraint which governs shape-changing actuation in these sheets. We then highlight the richness of shapes amenable to this constraint through two broad classes of examples which we term nonisometric origami and lifted surfaces. Finally, we comment on the derivation of the metric constraint, which arises from energy minimization in the interplay of stretching, bending, and heterogeneity in these sheets.