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Journal ArticleDOI

Programming curvature using origami tessellations

01 May 2016-Nature Materials (Nature Publishing Group)-Vol. 15, Iss: 5, pp 583-588
TL;DR: In this article, scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature.
Abstract: Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom collapsible structures-we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, as well as the quantification of the energetic and material cost of doing so.
Citations
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Journal ArticleDOI
TL;DR: In this article, the design principles leading to these properties are identified and discussed, in particular, linear and mechanism-based metamaterials (such as origami-based and kirigami based metammaterials), harnessing instabilities and frustration, and topological and nonlinear metam materials.
Abstract: Mechanical metamaterials exhibit properties and functionalities that cannot be realized in conventional materials. Originally, the field focused on achieving unusual (zero or negative) values for familiar mechanical parameters, such as density, Poisson's ratio or compressibility, but more recently, new classes of metamaterials — including shape-morphing, topological and nonlinear metamaterials — have emerged. These materials exhibit exotic functionalities, such as pattern and shape transformations in response to mechanical forces, unidirectional guiding of motion and waves, and reprogrammable stiffness or dissipation. In this Review, we identify the design principles leading to these properties and discuss, in particular, linear and mechanism-based metamaterials (such as origami-based and kirigami-based metamaterials), metamaterials harnessing instabilities and frustration, and topological metamaterials. We conclude by outlining future challenges for the design, creation and conceptualization of advanced mechanical metamaterials.

992 citations

Journal ArticleDOI
Yaqing Liu1, Ke He1, Geng Chen1, Wan Ru Leow1, Xiaodong Chen1 
TL;DR: This review covers the smart designs of structural materials inspired by natural materials and their utility in the construction of flexible devices, and summarizes structural materials that accommodate mechanical deformations, which is the fundamental requirement for flexible devices to work properly in complex environments.
Abstract: Exciting advancements have been made in the field of flexible electronic devices in the last two decades and will certainly lead to a revolution in peoples’ lives in the future. However, because of the poor sustainability of the active materials in complex stress environments, new requirements have been adopted for the construction of flexible devices. Thus, hierarchical architectures in natural materials, which have developed various environment-adapted structures and materials through natural selection, can serve as guides to solve the limitations of materials and engineering techniques. This review covers the smart designs of structural materials inspired by natural materials and their utility in the construction of flexible devices. First, we summarize structural materials that accommodate mechanical deformations, which is the fundamental requirement for flexible devices to work properly in complex environments. Second, we discuss the functionalities of flexible devices induced by nature-inspired stru...

518 citations

Journal ArticleDOI
TL;DR: A review of the latest progress and trends in methods for fabricating 3D mesostructures, beginning with the development of advanced material inks for nozzle-based approaches to 3D printing and new schemes for 3D optical patterning, can be found in this article.
Abstract: A rapidly expanding area of research in materials science involves the development of routes to complex 3D structures with feature sizes in the mesoscopic range (that is, between tens of nanometres and hundreds of micrometres). A goal is to establish methods for controlling the properties of materials systems and the function of devices constructed with them, not only through chemistry and morphology, but also through 3D architectures. The resulting systems, sometimes referred to as metamaterials, offer engineered behaviours with optical, thermal, acoustic, mechanical and electronic properties that do not occur in the natural world. Impressive advances in 3D printing techniques represent some of the most broadly recognized developments in this field, but recent successes with strategies based on concepts in origami, kirigami and deterministic assembly provide additional, unique options in 3D design and high-performance materials. In this Review, we highlight the latest progress and trends in methods for fabricating 3D mesostructures, beginning with the development of advanced material inks for nozzle-based approaches to 3D printing and new schemes for 3D optical patterning. In subsequent sections, we summarize more recent methods based on folding, rolling and mechanical assembly, including their application with materials such as designer hydrogels, monocrystalline inorganic semiconductors and graphene. Emerging materials and methods for fabricating 3D micro- and nanostructures provide powerful capabilities of relevance across diverse areas of technology. This Review highlights the latest results and future trends associated with the most powerful methods in 3D printing, folding and assembly.

448 citations

Journal ArticleDOI
TL;DR: A discussion of the strategies in materials innovation and structural design to build soft electronic devices and systems is provided and perspectives on the key challenges and future directions of this field are presented.
Abstract: Soft electronics are intensively studied as the integration of electronics with dynamic nonplanar surfaces has become necessary. Here, a discussion of the strategies in materials innovation and structural design to build soft electronic devices and systems is provided. For each strategy, the presentation focuses on the fundamental materials science and mechanics, and example device applications are highlighted where possible. Finally, perspectives on the key challenges and future directions of this field are presented.

417 citations

Journal ArticleDOI
TL;DR: A set of concepts for morphable 3D mesostructures in diverse materials and fully formed planar devices spanning length scales from micrometres to millimetres is introduced.
Abstract: Three-dimensional (3D) structures capable of reversible transformations in their geometrical layouts have important applications across a broad range of areas. Most morphable 3D systems rely on concepts inspired by origami/kirigami or techniques of 3D printing with responsive materials. The development of schemes that can simultaneously apply across a wide range of size scales and with classes of advanced materials found in state-of-the-art microsystem technologies remains challenging. Here, we introduce a set of concepts for morphable 3D mesostructures in diverse materials and fully formed planar devices spanning length scales from micrometres to millimetres. The approaches rely on elastomer platforms deformed in different time sequences to elastically alter the 3D geometries of supported mesostructures via nonlinear mechanical buckling. Over 20 examples have been experimentally and theoretically investigated, including mesostructures that can be reshaped between different geometries as well as those that can morph into three or more distinct states. An adaptive radiofrequency circuit and a concealable electromagnetic device provide examples of functionally reconfigurable microelectronic devices.

273 citations

References
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Book ChapterDOI

[...]

01 Jan 2012

139,059 citations

Journal ArticleDOI
14 May 1998-Nature
TL;DR: In this paper, the authors describe the appearance of complex, ordered structures induced by the buckling of thin metal films owing to thermal contraction of an underlying substrate, and account qualitatively for the size and form of the patterned features in terms of the nonuniform stresses developed in the film near steps on the polymer substrate.
Abstract: Spontaneous generation of complex order in apparently simple systems is both arresting and potentially useful1,2,3,4,5,6,7,8,9,10,11. Here we describe the appearance of complex, ordered structures induced by the buckling of thin metal films owing to thermal contraction of an underlying substrate. We deposit the films from the vapour phase on a thermally expanded polymer (polydimethylsiloxane, PDMS). Subsequent cooling of the polymer creates compressive stress in the metal film that is relieved by buckling with a uniform wavelength of 20–50 micrometres. The waves can be controlled and orientated by relief structures in the surface of the polymer, which can set up intricate, ordered patterns over large areas. We can account qualitatively for the size and form of the patterned features in terms of the non-uniform stresses developed in the film near steps on the polymer substrate. This patterning process may find applications in optical devices such as diffraction gratings and optical sensors, and as the basis for methods of strain analysis in materials.

2,158 citations

Journal ArticleDOI
08 Aug 2014-Science
TL;DR: Working with the Miura-ori tessellation, it is found that each unit cell of this crease pattern is mechanically bistable, and by switching between states, the compressive modulus of the overall structure can be rationally and reversibly tuned.
Abstract: Although broadly admired for its aesthetic qualities, the art of origami is now being recognized also as a framework for mechanical metamaterial design. Working with the Miura-ori tessellation, we find that each unit cell of this crease pattern is mechanically bistable, and by switching between states, the compressive modulus of the overall structure can be rationally and reversibly tuned. By virtue of their interactions, these mechanically stable lattice defects also lead to emergent crystallographic structures such as vacancies, dislocations, and grain boundaries. Each of these structures comes from an arrangement of reversible folds, highlighting a connection between mechanical metamaterials and programmable matter. Given origami’s scale-free geometric character, this framework for metamaterial design can be directly transferred to milli-, micro-, and nanometer-size systems.

719 citations

Journal ArticleDOI
TL;DR: This paper describes two folded metamaterials based on the Miura-ori fold pattern, where the fold pattern provides a negative Poisson’s ratio for in-plane deformations and a positive Poisson's ratio for out-of-plane bending.
Abstract: This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson's ratio for in-plane deformations and a positive Poisson's ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer.

678 citations

Book
16 Jul 2007
TL;DR: Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from high school students to researchers.
Abstract: How can linkages, pieces of paper, and polyhedra be folded? The authors present hundreds of results and over 60 unsolved 'open problems' in this comprehensive look at the mathematics of folding, with an emphasis on algorithmic or computational aspects. Folding and unfolding problems have been implicit since Albrecht Drer in the early 1500s, but have only recently been studied in the mathematical literature. Over the past decade, there has been a surge of interest in these problems, with applications ranging from robotics to protein folding. A proof shows that it is possible to design a series of jointed bars moving only in a flat plane that can sign a name or trace any other algebraic curve. One remarkable algorithm shows you can fold any straight-line drawing on paper so that the complete drawing can be cut out with one straight scissors cut. Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from high school students to researchers.

509 citations