Session F57: Origami and Kirigami Metamaterials

Towards a theory of self-folding

The physics of self-assembly of particles, self-folding of protein polymers and self-folding of sheets are very different. However, the design question shows striking similarities across these fields. In all of these fields, a given program (e.g., a protein sequence or a crease pattern) can generally fold into many undesired structures or kinetic traps. Conversely, many different programs can fold into the same desired structure. Hence, a common challenge is finding the best program to robustly achieve a given structure in the real world. Here, we generalize lessons learned in protein folding and self-assembly in a way that applies to folding sheets. We draw parallels to recent results for sheets by various researchers. We highlight ideas that have not yet been explored for sheets such as heterogeneous folding stiffness, controlled nucleation and multi-functional adaptive designs.   

Mechanical responce of Kirigami sheet materials

Kirigami is a technique for cutting of a sheet to realize some complex deformation of sheet materials. With a large number of slits, sheet materials can be stretched far beyond the original failure strain. It means that we can make a hard sheet flexible with simple “Kirigami” processing.
In this study, we perform experiments to elucidate the mechanical response of Kirigami structure from a fundamental point of view. We created a sample with one column of the kirigami structure and apply a tensile force. The overall relation between elongation and force which we measured is similar to the one typically observed in plastic materials. This behavior is divided into three regimes: (1) an initial linear elastic region, (2) a plateau region, and (3) a hardening region just before breakage. From this mechanical response, we see that high extensibility, which is a feature of Kirigami structure, emerges as a result of out-of-plane (three-dimensional) deformation that follows
in-plane (two-dimensional) deformation. This change in the mode of deformation defines the transition point. In this presentation, we focus on the initial region and discuss scaling laws demonstrating a good agreement between theory and experiment. [Ref. Isobe and Okumura, Sci. Rep. 6, 24758 (2016).]   

Bidirectional Folding with Nanoscale Sheets for Autonomous Micro-Origami

We present micron sized self-folding devices that consist of nanometer-thin metal oxide bilayers, built with conventional semiconductor fabrication methods. A bending response originating from strain differentials within these bilayer stacks is used as the fold actuation mechanism. This strain differential induced bending is controlled by ion exchange reactions in our nanoscale sheets, which can produce radii of curvature at the order of 10 um within seconds. By lithographically patterning these sheets, we localize the bending and create microscale devices that can sense chemical changes in their environment and respond by changing configurations according to prescribed mountain-valley fold patterns. Finally, we show that our fabrication approach offers a range of chemical, electrical and biological functions as well as a path to sequential folding through the programming of stacks.   

Circular kirigami structures: from linear elasticity to geometrical limits

Traditionally used for decorative objects, Kirigami structures are currently found in technological applications such as stretchable electronics. Relevant cutting designs indeed promote the apparent stretching of a stiff sheet through the actual bending of the structure at the scale of the cuts. However large-scale deformations are not limited to in-plane stretching. We show how out-of-plane 3D shapes are obtained by cutting alternate arcs in a 2D sheet. Within the limit of linear deformations, we rationalize the appropriate design of the axisymmetric cutting patterns leading to cone, bowl, trumpet or more complex shapes. We also track the geometrical limit corresponding to a full stretching of the structure. Is it possible to maximize the extension or the volume of the 3D structure? What is the range of 3D topographies obtained with such kirigami process?   

Kirigami Actuators

Inspired by the Japanese art of kirigami, we introduce new ways of modify thin sheets of material to craft dynamical assembling of complex shapes for mechanical actuation. We exploit the fundamental principles of this art through careful tuning of the geometry and topology of these cuts on thin sheets and propose the design of actuators that scale from macroscopic sheets of mylar to atomically thin 2D materials (graphene and MoS₂). By understanding the mechanics of a single cut on a sheet, we can take advantage of the nonlinear and anisotropic responses to external forces to generate four fundamental modes of linear actuation: roll, pitch, yaw, and lift, essentially creating a new class of mechanical metamaterials. Our model shows that the dependence of the sheet deflections on sheet thickness is of a higher order, thus providing an explanation for the observed invariance in kirigami actuator behaviors from the macroscale to the nanoscale.   

An Origami-inspired Mechanical Metamaterial with Graded Stiffness

Origami-inspired mechanical metamaterials are often made up of individual repeat units, the folding and relative geometry of which determine the overall material properties. If these units are identical, then the mechanical properties and behaviour of the material is uniform throughout, meaning that it is not able to adapt to non-uniform environments. Here we create and study a metamaterial, based on the Miura-ori folding pattern, which has a varying geometry and graded stiffness through the material. Using kinematic analysis, we show how geometric parameters of the folding pattern can be varied to create both rigid foldable and self locking stages. We demonstrate both experimentally and numerically that the metamaterial can achieve periodically graded stiffness when subjected to out-of-plane compression, and the responses can be tuned by changing the underlying geometric design. We obtain a metamaterial with superior energy absorption capability compared with uniform tessellating repeat units, and anticipate that this strategy could be extended to other metamaterials to impart them with non-uniform and graded mechanical properties.   

Hidden symmetries permit folding of all triangulated origami

Origami--thin sheets that fold along preset crease patterns--is at once an art form, an important technology for forming mechanical structures and a mathematically difficult problem of determining the folds permitted by a particular pattern. Origami devices are now being realized at the difficult-to-control atomic scale, motivating the question of which types of folding motions realized by crease patterns are also possible under broader classes of creases. We consider periodic triangulated origami of no engineered symmetry, and show that the geometry of the origami surface leads to hidden symmetries that link rigid-body motions of the sheet to force-bearing modes, which are then linked to folding motions. These folding patterns extend nonlinearly, permitting the origami to fold into cylindrical sections that can bend, twist and strain through particular configuration spaces. Our results also apply to related systems that, like triangulated origami, have balanced numbers of constraints and degrees of freedom, such as kirigami (cut origami) and continuum sheets, and can serve as the basis for a broad new class of deployable origami structures.   

Tuning the mechanical properties and crumpling temperature of thermalised elastic sheets with perforations

Thermalised elastic membranes without distant self-avoidance are believed to undergo a crumpling transition when the microscopic bending stiffness is comparable to kT. Most potential physical realizations of such membranes have a bending stiffness well in excess of experimentally achievable temperatures and are therefore unlikely ever to access the crumpling regime. We propose a mechanism to tune the crumpling transition by altering the membrane's geometry and topology. We have carried out extensive MD simulations of perforated sheets with a dense array of holes and observed that the critical temperature is controlled by the total fraction of removed area, independent of the precise arrangement and size of the individual holes. The critical exponents for the perforated membrane are compatible with those of the standard crumpling transition. We also explore crumpling in the polymer-like limit of a thin frame and make experimentally relevant predictions for graphene sheets.

[1] D. Yllanes, S. Bhabesh, D.R. Nelson, M.J. Bowick arXiv:1705.07379. Nat. Comm (in press) 2017. DOI: 10.1038/s41467-017-01551-y   

Elastic buckling control of cylindrical shells using origami patterns

Elastic buckling of thin cylindrical shells, mainly due to loss of local stability, is difficult to be precisely predicted. Here we report a cylinder which has unfolded origami pattern embedded on the surface, with the aim of control its buckling behaviors. Two kind of patterns, a straight-crease diamond pattern, and a curved-crease origami pattern with elastica surface, were studied. We found the buckling modes of the cylinder were sensitively affected by pattern geometric parameters through quasi-static axial compression. Furthermore, the buckled configurations could be accurately controlled if appropriate guidance creases was selected. Finally, the snap-through behavior of the repetitive lobes formed on the cylinders was investigated, where the variation in strain energy during the buckling process was obtained. By using the proposed method, we are able to accurately design the buckled configurations of a cylinder upon specific requirements.   

Locomotion of a kirigami-skinned soft crawler

Nature offers many examples of slender limbless organisms that take advantage of both the flexibility of their body and the frictional properties of their skin to efficiently move and explore the surrounding space. Inspired by the friction-assisted locomotion of snakes, we design a pneumatically actuated soft crawling robot combined with a stretchable kirigami skin with tunable frictional properties. We demonstrate that the flexibility and the directional friction anisotropy of the skin are two main factors affecting the locomotion efficiency of soft crawlers. By integrating the potentials of kirigami-inspired architected materials, the proposed design significantly simplifies the inputs required for actuation of soft robots.   

Non-flat origami: branch splitting and tristable vertices.

Flat 4-vertices have two continuous folding branches which meet at the flat state. Here we show how these branches split into two separate branches for non-flat 4-vertices. Nevertheless, we can jump between these branches via a tunable pop-through transition. Augmenting these vertices with torsional springs, we create tristable origami.   

Reconfiguration Mechanisms of Humidity-Driven Origami Networks

Adaptive materials that respond mechanically to a stimulus are of interest for a wide range of technologies, including soft robotics, responsive optoelectronics and environmental control systems. Typically these materials demonstrate relatively simple mechanical responses such as shrinking, expanding, or bending. The art of origami, where localized deformation at folds can generate complex structures and mechanisms, provides an opportunity to harness the mechanical response of adaptive materials and channel it into novel mechanical behavior. Using networks of waterbomb and chomper origami mechanisms within a humidity sensitive material, PEDOT:PSS, we demonstrate that the placement of the adaptive material dictates whether a structure undergoes fold inversion or reversible reconfiguration, such as snap-through between bistable states. Design and performance behavior is understood by modeling the response of the origami system to the application of point, linear or areal forces arising from the adaptive material’s shape, location and response to the local environment. Following these principles, we also demonstrate autonomous reconfiguration of complex origami structures in response to local humidity gradients.   

Non-linear Mechanics of Kirigami

Kirigami patterns generate non-trivial three dimensional behavior from perforated sheets, and so offer a promising means for developing mechanical metamaterials. To create a generic account of the mechanical behavior of kirigami, we study the unit cell of a typical kirigami structure, an isolated frame. The mechanical behavior of the entire sheet may then be understood in terms of the coupling of many individual frames. In simple experiments using mylar and paper, we study the scaling of the force response and the buckling behavior with respect to geometric parameters such as hole size and sheet thickness. Because real applications may involve sheets which are initially deformed, we then study how the mechanical response changes in the presence of crumpling. Finally, we study how the behavior of individual frames couples when frames are arranged in chains or sheets.