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Origami, the ancient Japanese art of paper folding, is not only an inspiring technique to create sophisticated shapes, but also a surprisingly powerful method to induce nonlinear mechanical properties. Over the last decade, advances in crease design, mechanics modeling, and scalable fabrication have fostered the rapid emergence of architected origami materials. These materials typically consist of folded origami sheets or modules with intricate 3D geometries, and feature many unique and desirable material properties like auxetics, tunable nonlinear stiffness, multistability, and impact absorption. Rich designs in origami offer great freedom to design the performance of such origami materials, and folding offers a unique opportunity to efficiently fabricate these materials at vastly different sizes. Here, recent studies on the different aspects of origami materials—geometric design, mechanics analysis, achieved properties, and fabrication techniques—are highlighted and the challenges ahead discussed. The synergies between these different aspects will continue to mature and flourish this promising field.

 

Structures with adaptive capabilities offer many potentials to achieve future needs in efficiency, reliability, and intelligence. To this end, bistable CFRP (Carbon Fibre Reinforced Polymers) composites with asymmetric fiber layout are a promising concept that has shown shape morphing capabilities that adapt to the changes in the environment such as external forces and moments. This adaptability opens them to endless application potentials, ranging from small micro-switches to large airfoil sections in airplane wings or wind turbine blades. To harness this potential, it is essential to predict these composites’ physical shapes and behavior accurately. To this end, Hyer and Dano devised the first analytical model based on the concepts of Classical Lamination Theory, and this model has become the cornerstone of almost all subsequent studies. However, this theory uses Kirchoff’s theory of thin plates that are limited by several assumptions. As a result, Hyer’s theory can predict the overall shape of these laminates but lacks accuracy. A reason for this model’s underperformance is that it ignores the inter-laminar stresses and strains, but such stresses/strains play a vital role in the balance of the overall stress field and are found significantly higher near the free edges. To overcome these fundamental limitations, we propose a new analytical approach by combining the Reissner-Mindlin theory with concepts from the Classical Lamination Theory. This new model introduces in-plane rotations as two additional degrees of freedom. Thus, it has five independent variables compared to only three in Hyer and Dano’s model and its derivatives. Hence, we have a more complex but more accurate model. This paper outlines our new analytical approach by 1) introducing these two additional degrees of freedom; 2) selecting appropriate polynomial approximations; 3) formulating inter-laminar stresses that are functions of these added rotations; and 4) incorporating these inter-laminar stresses in the potential energy equation. By comparing this model’s prediction with the finite element simulation results, we found the new model slightly under predicts the laminate deformation, but the overall accuracy is promising, as evidenced by high R-squared correlation. 

This study examines the transverse elastic wave propagation bandgap in a buckled kirigami sheet. Kirigami — the ancient art of paper cutting — has become a design and fabrication framework for constructing metamaterials, robotics, and mechanical devices of vastly different sizes. For the first time, this study focuses on the wave propagation in a buckled kirigami sheet with uniformly distributed parallel cuts. When we apply an in-plane stretching force that exceeds a critical threshold, this kirigami sheet buckles and generates an out-of-plane, periodic deformation pattern that can change the propagation direction of passing waves. That is, waves entering the buckled Kirigami unit cells through its longitudinal direction can turn to the out-of-plane direction. As a result, the stretched kirigami sheet shows wave propagation band gaps in specific frequency ranges. This study formulates an analytical model to analyze the correlation between such propagation bandgap and the kirigami geometry. This model first simplifies the complex shape of buckled kirigami by introducing “virtual” folds and flat facets in between them. Then it incorporates the plane wave expansion method (PWE) to calculate the dispersion relationship, which shows that the periodic nature of the buckled kirigami sheet is sufficient to create Bragg scattering propagation bandgap. This study’s results could open up new dynamic functionalities of kirigami as a versatile and multi-functional structural system. 

Soft pneumatic actuators have become indispensable for many robotic applications due to their reliability, safety, and design flexibility. However, the currently available actuator designs can be challenging to fabricate, requiring labor-intensive and time-consuming processes like reinforcing fiber wrapping and elastomer curing. To address this issue, we propose to use simple-to-fabricate kirigami skins—plastic sleeves with carefully arranged slit cuts—to construct pneumatic actuators with pre-programmable motion capabilities. Such kirigami skin, wrapped outside a cylindrical balloon, can transform the volumetric expansion from pneumatic pressure into anisotropic stretching and shearing, creating a combination of axial extension and twisting in the actuator. Moreover, the kirigami skin exhibits out-of-plane buckling near the slit cut, which enables high stretchability. To capture such complex deformations, we formulate and experimentally validates a new kinematics model to uncover the linkage between the kirigami cutting pattern design and the actuator’s motion characteristics. This model uses a virtual fold and rigid-facet assumption to simplify the motion analysis without sacrificing accuracy. Moreover, we tested the pressure-stroke performance and elastoplastic behaviors of the kirigami-skinned actuator to establish an operation protocol for repeatable performance. Analytical and experimental parametric analysis shows that one can effectively pre-program the actuator’s motion performance, with considerable freedom, simply by adjusting the angle and length of the slit cuts. The results of this study can establish the design and analysis framework for a new family of kirigami-skinned pneumatic actuators for many robotic applications. 

Thin bistable composite laminates can be used for shape morphing applications by virtue of their material properties and asymmetric ply layup. These laminates are called bistable because they can be snapped into two or more stable shapes. A single bistable patch can result in simple cylindrical shapes and when multiple such patches are assembled into a single multi-patch laminate they result in more complex shapes and multiple stable shapes that can find wide practical use in shape morphing applications. Analytical models exist that can approximate the stable shapes of the laminates from the input of material properties and laminate geometry. And these models correlate with FEA and experiment to a satisfactory degree and could be used for the design of multi patch laminates. In this research, we make use of these analytical models that solve for a four-patch grid laminate and create a design method based on optimization to solve the reverse problem to arrive at the laminate parameters given the target shape(s). Two approaches are presented wherein one targets a single stable shape and the other targets two stable shapes which are the shapes before and after snap through. This work would be useful to understand how multi-patch laminates could be designed using optimization. 

Bistability is exhibited by an object when it can be resting in two stable equilibrium states. Certain composite laminates exhibit bistability by having two stable curvatures of opposite sign with the two axes of curvature perpendicular to each other. These laminates can be actuated from one state to the other. The actuation from the original post-cure shape to the second shape is called as ‘snap-through’ and the reverse actuation is called as ‘snap-back’. This phenomenon can be used in applications for morphing structures, energy harvesting, and other applications where there is a conflicting requirement of a structure that is load-carrying, light, and shape-adaptable. MW Hyer first reported this phenomenon in his paper in 1981. He found that thin unsymmetric laminates do not behave according to the predictions of the Classical Lamination Theory (CLT). The CLT is a linear theory and predicts the post-cure shape of thin unsymmetric laminates to be a saddle. MW Hyer developed a non-linear method called the “Extended Classical Lamination Theory” which accurately predicted the laminate to have two cylindrical shapes. Since then, a number of researchers have tried to identify the key parameters affecting the behavior of such laminates. Geometric parameters such as stacking sequence, fibre orientation, cure cycle, boundary conditions, and force of actuation, have all been studied. The objective of this research is to define a relation between the length, width and thickness of square and rectangular laminates required to achieve bistability. Using these relations, a 36 in × 36 in bistable laminate is fabricated with a thickness of 30 CFRP layers. Also, it is proved that a laminate does not lose bistability with an increase in aspect ratio, as long as both sides of the rectangular laminate are above a certain ‘critical length’. A bistable laminate with dimensions of 2 in × 50 in is fabricated. Further, for laminates that are bistable, it is necessary to be able to predict the curvature and force required for actuation. Therefore, a method is developed which allows us to predict the curvature of both stable shapes, as well as the force of actuation of laminates for which the thickness and dimensions are known. Finite Element Analysis is used to carry out the numerical calculations, which are validated by fabricating laminates. The curvature of these laminates is measured using a profilometer and the force of actuation is recorded using a universal test set-up. 

Soft pneumatic actuators have found many applications in robotics and adaptive structures. Traditionally, these actuators are constructed by wrapping layers of reinforcing helical fibers around an elastomeric tube. This approach is versatile and robust, but it suffers from a critical disadvantage: cumbersome fabrication procedures. Wrapping long helical filaments around a cylindrical tube requires expensive equipment or excessive manual labor. To address this issue, we propose a new approach towards designing and constructing pneumatic actuators by exploiting the principle of kirigami, the ancient art of paper cutting. More specifically, we use “kirigami skins” — plastic sleeves with carefully arranged slit cuts — to replace the reinforcing helical fibers. This paper presents an initial investigation on a set of linear extension actuators featuring kirigami skins with a uniform array of cross-shaped, orthogonal cuts. When under internal pressurization, the rectangular-shaped facets defined by these cuts can rotate and induce the desired extension motion. Through extensive experiments, we analyze the elastic and plastic deformations of these kirigami skins alone under tension. The results show strongly nonlinear behaviors involving both in-plane facet rotation the out-of-plane buckling. Such a deformation pattern offers valuable insights into the actuator’s performance under pressure. Moreover, both the deformation characteristics and actuation performance are “programmable” by tailoring the cut geometry. This study lays down the foundation for constructing more capable Kirigami-skinned soft actuators that can achieve sophisticated motions.