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
A Study of the Multi-Stability in a Non-Rigid Stacked Miura-Origami Cellular Mechanism
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.
more »
« less
- Award ID(s):
- 1751449
- NSF-PAR ID:
- 10322848
- Date Published:
- Journal Name:
- Proceedings of the ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
- Volume:
- 8B
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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.more » « less
-
Origami — the ancient art of paper folding — has been widely adopted as a design and fabrication framework for many engineering applications, including multi-functional structures, deployable spacecraft, and architected materials. These applications typically involve complex and dynamic deformations in the origami facets, necessitating high-fidelity models to better simulate folding-induced mechanics and dynamics. This paper presents the formulation and validation of such a new model based on the Absolute Nodal Coordinate Formulation (ANCF), which exploits the tessellated nature of origami and describes it as an assembly of flexible panels rotating around springy creases. To estimate the crease folding, we mathematically formulate a “torsional spring connector” in the framework of ANCF and apply it to the crease nodes, where the facets meshed by ANCF plate elements are interconnected. We simulate the dynamic folding of a Miura-ori unit cell and compare the results with commercial finite element software (ABAQUS) to validate the modeling accuracy. The ANCF model can converge using significantly fewer elements than ABAQUS without sacrificing accuracy. Therefore, this high-fidelity model can help deepen our knowledge of folding-induced mechanics and dynamics, broadening the appeals of origami in science and engineering.more » « less
-
Origami structures with a large number of excess folds are capable of storing distinguishable geometric states that are energetically equivalent. As the number of excess folds is reduced, the system has fewer equivalent states and can eventually become rigid. We quantify this transition from a floppy to a rigid state as a function of the presence of folding constraints in a classic origami tessellation, Miura-ori. We show that in a fully triangulated Miura-ori that is maximally floppy, adding constraints via the elimination of diagonal folds in the quads decreases the number of degrees of freedom in the system, first linearly and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via a redundancy in the assignment of constraints, and the degrees of freedom depend on constraint density in a scale- invariant manner. A percolation transition in the redundancy in the constraints as a function of constraint density suggests how excess folds in an origami structure can be used to store geometric information in a scale-invariant way.more » « less
-
more » « less
Origami structures with a large number of excess folds are capable of storing distinguishable geometric states that are energetically equivalent. As the number of excess folds is reduced, the system has fewer equivalent states and can eventually become rigid. We quantify this transition from a floppy to a rigid state as a function of the presence of folding constraints in a classic origami tessellation, Miura-ori. We show that in a fully triangulated Miura-ori that is maximally floppy, adding constraints via the elimination of diagonal folds in the quads decreases the number of degrees of freedom in the system, first linearly and then nonlinearly. In the nonlinear regime, mechanical cooperativity sets in via a redundancy in the assignment of constraints, and the degrees of freedom depend on constraint density in a scale-invariant manner. A percolation transition in the redundancy in the constraints as a function of constraint density suggests how excess folds in an origami structure can be used to store geometric information in a scale-invariant way.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1115/DETC2021-67670
