Our group focus on studying the mechanics of folded thin-sheet structures on various scales. We studies modeling techniques, fabrication methods, and unique mechanical behaviors of such structures. Here are a list of ongoing projects:
- Functional Small Scale Actuators with Origami Inspired Structures
- Behavior of Curved-Crease Origami Structures
- Using Tunable Origami for Active Energy Absorption
- Bistable Behavior of Origami Hypar
The small scale actuator project is funded by DARPA. In this project, our group is studying the potential of including origami inspired assemblages in the design of various MEMS (micro-electro-mechanical system) devices. The initial goal is to fabricate the folding device using combined PZT / Active Polymer system to complex assembling of intricate 3D structures.
Principal Investigator: Prof. Evgueni T. Filipov,
Subcontracted Investigator: Prof. Kenn Oldham,
Graduate Student: Maria Redoutey, Yi ZHU, Mira Diab El Harakeh.
Undergraduate Student: Kevin Turaczy.
The researchers of the project acknowledge support from DARPA Grant D18AP00071. The summary and published papers reflect the views and position of the authors, and not necessarily those of the funding entities.
This project explores the mechanical behavior of curved-crease origami tessellation. Unlike traditional origami, these patterns are created by folding thin sheets about curved creases. The resulting geometries offer unique structural properties that can be exploited in engineering design. This research aims to discover the underlying principles that govern the behavior of curved-crease origami through a variety of modeling techniques and theories so that engineers may benefit from their properties.
Energy absorption devices are widely used to mitigate damage from collisions and impact loads. Due to the inherent uncertainty of possible impact characteristics, passive energy absorbers with fixed mechanical properties are not capable of serving in different application scenarios. Therefore, origami-inspired structures, which possess the ability to reconfigure and deploy, are a qualified candidate for a novel active design. In this work, we apply the constrained zipper-coupled Miura-ori tubes (deployable and stiff after locking) as the basis to a tubular energy absorber. Numerical and experimental (static and dynamic) studies are performed to quantify the response of these novel structures. This work shows that the reconfigurable origami could change their stiffness and the total amount of energy they absorb. These behaviors are suitable for creating systems with on-demand properties that adapt to different impact scenarios.
The research team of this project acknowledge funding from the ZF Automotive Research Award and the Office of Naval Research (Grant N00014-18-1-2015). J.R. acknowledges support from the SURE program at the University of Michigan.
This project explores the mechanical behavior of the origami hyperbolic paraboloid (hypar). The hypar is created from a flat and developable sheet, however, when folded, it forms a bistable three dimensional structure resembling a hyperbolic paraboloid with non-zero Gaussian curvature. We have used experiments to evaluate the global and local behaviors of the structure, which are unique from other bistable origami systems. For the system to reconfigure between the two stable states, each crease first unfolds and then refolds into the new stable geometry. Our work shows that this bistable transition is also affected by stretching of the thin sheet, local buckling in the system, and nonlinear behaviors in the material. We have reinforced our understanding of the hypar behavior by establishing an analytical model that can simulate the kinematics, the buckling, and the force–displacement behavior of the structure. In addition to uncovering the mechanics of the hypar, we have also motivated the future adoption of these systems into functional and practical applications. Because hypars can be created from thin developable sheets, they are suitable for efficient manufacturing through flat patterning and self-assembly. The project has also explored topics for future extension and introduces hypar chains, where multiple hypars are connected in series to achieve multistability.
- E. T. Filipov, M Redoutey. (2018) Mechanical characteristics of the bistable origami hypar, Extreme Mechanics Letters 25, 16-26.
Prof. E.T. Filipov’s previous research on folded structures focuses on mechanics of origami tubular structures.
Analytical models for thin-sheet structures
We have improved a model for the analysis of origami structures that consist of flat panels interconnected by a pattern of prescribed fold lines. This bar and hinge model, first introduced by Schenk and Guest (2011) can capture the fundamental behaviors of thin folded sheet structures. The model consists of three components: (1) elastic bar elements that simulate the stretching and shear stiffness thin panels; (2) rotational hinges that simulate folding of the panels; and (3) rotational hinges that simulate folding along the more flexible prescribed fold lines. We have made the model scalable, and have incorporated material characteristics such as the elastic modulus, Poisson’s ratio, and thickness of the thin sheet. Although this model is not as as accurate as a detailed finite element (FE) model it provides several useful advantages. The model is easy to implement, easy to use, it provides insightful results, and it is faster than FE analyses. The efficiency of the model makes it suitable for extensions to parametric studies, optimization or various specialized analyses.
Deployable coupled tube structures
We have explored a variety of origami tube systems and assemblages. The basic type of tube is constructed by placing two symmetric Miura-ori sheets together (see Tachi 2009). The tube is rigid and flat foldable meaning it can fully unfold from a flattened state with deformations occurring only at the fold lines. We used eigenvalue and structural cantilever analysis to investigate and compare different geometries of tubes and coupled tube systems. The “zipper”-coupled tube system (shown on the left) yields an unusually large eigenvalue band-gap that represents a unique difference in stiffness between deformation modes. The structure has only one flexible mode through which it can deploy, yet it is significantly stiffer for all other bending and twisting type modes. The deployment motion is permitted by the flexible bending the thin sheet along the prescribed fold lines, however all other modes require the significantly stiffer stretching and shear of the thin sheet. The zipper-couped tubes have the advantages of deployable origami, but also the stiffening effect that is common in cellular/corrugated structures and materials.
Extensions from metamaterials to deployable architecture
Origami sheets and origami tubes can be coupled, combined, and arranged in a variety of methods to form new geometries and structures. We have shown different methods in which the zipper-coupled tubes can be assembled into cellular assemblages. By combining different types of coupled tubes together we can also enhance the structural characteristics of these systems. For example, the cubic cellular assemblage (shown top right) consists of zipper and aligned coupling, and has both space filling properties and the enhanced stiffness of the zipper tubes. This assemblage can have a variable asymmetrical stiffness depending on its configuration. Similarly, it is be possible to couple different geometries of tubes. To create a bridge type structure (shown bottom right), we use nearly square tubes to provide a smooth deck, and we use zippered zig-zag tubes to create a stiffer parapet. The deployable origami assemblages could lead to practical applications ranging in size from microscale metamaterials that harness the novel mechanical properties to large-scale deployable systems in engineering and architecture.
Publications related to this research:
- Filipov, E.T., Paulino G.H., and Tachi T. “Origami Tubes with Reconfigurable Polygonal Cross-Sections”. Proceedings of the Royal Society – A , Vol. 472, No. 2185, 20150607. See paper, details, and media coverage.
- Filipov, E.T., Tachi T., and Paulino G.H. (2015) “Origami Tubes Assembled Into Stiff, yet Reconfigurable Structures and Metamaterials,” Proceedings of the National Academy of Sciences USA , Vol. 112, No. 40, pp. 12321-12326. See paper, details, and media coverage.
- Filipov, E.T., Tachi, T., and Paulino, G.H. (2015). “Toward Optimization of Stiffness and Flexibility of Rigid, Flat-Foldable Origami Structures,” In Origami 6, Proc. of the 6th International Meeting on Origami Science, Mathematics, and Education (eds K Miura, T Kawasaki, T Tachi, R Uehara, RJ Lang, P Wang-Iverson), pp. 409–419. Providence, RI: American Mathematical Society.
Highlighted in PNAS commentary by Reis et al. 2015. Reported by: WXYZ TV – ABC News, Civil + Structural Engineer, Discovery News, Motherboard, City Lab, Fast Company, Gizmag, Phys.org, Science Daily, Space Daily, Gizmodo, Sydney Morning Herald, also more on zipper tubes and more on polygonal tubes.