Multi-stable structures have gathered extensive interest because they can provide a broad spectrum of adaptive functions for many engineering systems. Especially, origami sheets with a translational periodicity can be stacked and assembled to form a multi-stable cellular solid, which has emerged as a promising platform to design functional structures. This paper investigates the multi-stability characteristics of a non-rigid stacked Miura-origami mechanism consisting of Miura-ori sheets and accordion-shaped connecting sheets, focusing on the elemental unit cell. A nonlinear mechanical model based on the barhinge approach is established to quantitatively study the unit cell’s multi-stability with intentionally relaxed rigid-folding conditions. Results show that only two stable states are achievable in the unit cell with enforced rigid-folding kinematics. However, if one relaxes the rigid-folding conditions and allows the facet to deform (i.e. non-rigid folding), four stable states are reachable in the unit cell if the crease torsional stiffness of the connecting sheets becomes sufficiently larger than that of the Miura-ori sheets, or the stress-free folding angle deviates away from 0°. A close examination of the potential energy composition of the non-rigid unit cell provides a detailed principle underpinning the multi-stability. By showing the benefits of exploiting facet compliance, this study can become the building blocks for origami-based structures and material systems with a wider variety of novel functionalities.
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Magneto-origami structures: Engineering multi-stability and dynamics via magnetic-elastic coupling
Origami provides a flexible platform for constructing three-dimensional multi-stable mechanical metamaterials and structures. While possessing many interesting features originating from folding, the development of multi-stable origami structures is faced with tremendous demands for acquiring tunability and adaptability. Through an integration of origami folding with magnets, this research proposes a novel approach to synthesize and harness multi-stable
magneto-origami structures. Based on the stacked Miura-ori and the Kresling ori structures, we reveal that the embedded magnets could effectively tune the structure’s potential energy landscapes, which includes not only altering the position and the depth of the potential wells but essentially eliminating the intrinsic potential wells or generating new potential wells. Such magnet-induced evolutions of potential energy landscapes would accordingly change the origami structure’s stability profiles and the constitutive force–displacement relations. Based on proof-ofconcept prototypes with permeant magnets, the theoretically predicted effects of magnets are verified. The exploration is also extended to the dynamics realm. Numerical studies suggest that the incorporated magnets not only could translate the critical frequencies for achieving certain dynamical behaviors but also fundamentally adjust the frequency-amplitude relationship. Overall, this study shows that the proposed approach would provide a novel means to control the stability profile as well as the mechanics and dynamic characteristics of origami structures, and thus, inspire new innovations in designing adaptive mechanical metamaterials and structures.
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- Award ID(s):
- 1634545
- NSF-PAR ID:
- 10197884
- Date Published:
- Journal Name:
- Smart materials and structures
- ISSN:
- 1361-665X
- Page Range / eLocation ID:
- 17
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The Kresling truss structure, derived from Kresling origami, has been widely studied for its bi-stability and various other properties that are useful for diverse engineering applications. The stable states of Kresling trusses are governed by their geometry and elastic response, which involves a limited design space that has been well explored in previous studies. In this work, we present a magneto-Kresling truss design that involves embedding nodal magnets in the structure, which results in a more complex energy landscape, and consequently, greater tunability under mechanical deformation. We explore this energy landscape first along the zero-torque folding path and then release the restraint on the path to explore the complete two-degree-of-freedom behavior for various structural geometries and magnet strengths. We show that the magnetic interaction could alter the potential energy landscape by either changing the stable configuration, adjusting the energy well depth, or both. Energy wells with different minima endow this magneto-elastic structure with an outstanding energy storage capacity. More interestingly, proper design of the magneto-Kresling truss system yields a tri-stable structure, which is not possible in the absence of magnets. We also demonstrate various loading paths that can induce desired conformational changes of the structure. The proposed magneto-Kresling truss design sets the stage for fabricating tunable, scalable magneto-elastic multi-stable systems that can be easily utilized for applications in energy harvesting, storage, vibration control, as well as active structures with shape-shifting capability.more » « less
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Recently, multi-stable origami structures and material systems have shown promising potentials to achieve multi-functionality. Especially, origami folding is fundamentally a three-dimensional mechanism, which imparts unique capabilities not seen in the more traditional multi-stable systems. This paper proposes and analytically examines a multi-stable origami cellular structure that can exhibit asymmetric energy barriers and a mechanical diode behavior in compression. Such a structure consists of many stacked Miura-ori sheets of different folding stiffness and accordion-shaped connecting sheets, and it can be divided into unit cells that features two different stable equilibria. To understand the desired diode behavior, this study focuses on two adjacent unit cells and examines how folding can create a kinematic constraint onto the deformation of these two cells. Via estimating the elastic potential energy landscape of this dual cell system. we find that the folding-induced kinematic constraint can significantly increase the potential energy barrier for compressing the dual-cell structure from a certain stable state to another, however, the same constraint would not increase the energy barrier of the opposite extension switch. As a result, one needs to apply a large force to compress the origami cellular structure but only a small force to stretch it, hence a mechanical diode behavior. Results of this study can open new possibilities for achieving structural motion rectifying, wave propagation control, and embedded mechanical computation.more » « less
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Origami-inspired mechanical metamaterials could exhibit extraordinary properties that originate almost exclusively from the intrinsic geometry of the constituent folds. While most of current state of the art efforts have focused on the origami’s static and quasi-static scenarios, this research explores the dynamic characteristics of degree-4 vertex (4-vertex) origami folding. Here we characterize the mechanics and dynamics of two 4-vertex origami structures, one is a stacked Miura-ori (SMO) structure with structural bistability, and the other is a stacked single-collinear origami (SSCO) structure with lockinginduced stiffness jump; they are the constituent units of the corresponding origami metamaterials. In this research, we theoretically model and numerically analyze their dynamic responses under harmonic base excitations. For the SMO structure, we use a third-order polynomial to approximate the bistable stiffness profile, and numerical simulations reveal rich phenomena including small-amplitude intrawell, largeamplitude interwell, and chaotic oscillations. Spectrum analyses reveal that the quadratic and cubic nonlinearities dominate the intrawell oscillations and interwell oscillations, respectively. For the SSCO structure, we use a piecewise constant function to describe the stiffness jump, which gives rise to a frequencyamplitude response with hardening nonlinearity characteristics. Mainly two types of oscillations are observed, one with small amplitude that coincides with the linear scenario because locking is not triggered, and the other with large amplitude and significant nonlinear characteristics. The method of averaging is adopted to analytically predict the piecewise stiffness dynamics. Overall, this research bridges the gap between the origami quasi-static mechanics and origami folding dynamics, and paves the way for further dynamic applications of origami-based structures and metamaterials.more » « less
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Abstract Mechanical metamaterials inspired by the Japanese art of paper folding have gained considerable attention because of their potential to yield deployable and highly tunable assemblies. The inherent foldability of origami structures enlarges the material design space with remarkable properties such as auxeticity and high deformation recoverability and deployability, the latter being key in applications where spatial constraints are pivotal. This work integrates the results of the design, 3D direct laser writing fabrication, and in situ scanning electron microscopic mechanical characterization of microscale origami metamaterials, based on the multimodal assembly of Miura‐Ori tubes. The origami‐architected metamaterials, achieved by means of microfabrication, display remarkable mechanical properties: stiffness and Poisson’s ratio tunable anisotropy, large degree of shape recoverability, multistability, and even reversible auxeticity whereby the metamaterial switches Poisson’s ratio sign during deformation. The findings here reported underscore the scalable and multifunctional nature of origami designs, and pave the way toward harnessing the power of origami engineering at small scales.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1361-665X/ab524e
