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Self-folding origami, structures that are engineered flat to fold into targeted, three-dimensional shapes, have many potential engineering applications. Though significant effort in recent years has been devoted to designing fold patterns…

Soft Condensed Matter · Physics 2022-03-25 M. E. Lee-Trimble , Ji-Hwan Kang , Ryan C. Hayward , Christian D. Santangelo

Lattices and their underlying symmetries play a central role in determining the physical properties and applications of many natural and engineered materials. By bridging the lattice geometry and rigid-folding kinematics, this study…

Applied Physics · Physics 2019-09-18 Hongbin Fang , Suyi Li , Manoj Thota , Kon-Well Wang

The ability to transform a flat sheet into a complex three-dimensional structure is a fundamental test of physical intelligence. Unlike cloth manipulation, origami is governed by strict geometric axioms and hard kinematic constraints, where…

Graphics · Computer Science 2026-04-06 Yanjia Huang , Yunuo Chen , Ying Jiang , Jinru Han , Zhengzhong Tu , Yin Yang , Chenfanfu Jiang

We develop recursion equations to describe the three-dimensional shape of a sheet upon which a series of concentric curved folds have been inscribed. In the case of no stretching outside the fold, the three-dimensional shape of a single…

Soft Condensed Matter · Physics 2012-12-17 Marcelo A. Dias , Christian D. Santangelo

The ability to morph flat sheets into complex 3D shapes is extremely useful for fast manufacturing and saving materials while also allowing volumetrically efficient storage and shipment and a functional use. Direct 4D printing is a…

Graphics · Computer Science 2022-06-13 Bihui Zou , Chao Song , Zipeng He , Jaehyung Ju

The recent development of modular origami structures has ushered in a new era for active metamaterials with multiple degrees of freedom (multi-DOF). Notably, no systematic inverse design approach for volumetric modular origami structures…

Materials Science · Physics 2022-12-13 Kai Xiao , Xiang Zhou , Jaehyung Ju

As we enter the age of designer matter - where objects can morph and change shape on command - what tools do we need to create shape-shifting structures? At the heart of an elastic deformation is the combination of dilation and distortion,…

Soft Condensed Matter · Physics 2018-09-14 Douglas P. Holmes

We study the three-dimensional equilibrium shape of a shell formed by a deployed accordion-like origami, made from an elastic sheet decorated by a series of parallel creases crossed by a central longitudinal crease. Surprisingly, while the…

Soft Condensed Matter · Physics 2021-02-09 Théo Jules , Frédéric Lechenault , Mokhtar Adda-Bedia

The challenge in reconfigurable manipulation of sound waves using metasurfaces lies in achieving precise control over acoustic behavior while developing efficient and practical tuning methods for structural configurations. However, most…

Kirigami metamaterial sheets and tubes, owing to their capacity to undergo large elastic deformations while developing three-dimensional surface textures, have enormous potential as skins for soft robots. Here, we propose to use kirigami…

Soft Condensed Matter · Physics 2025-05-01 Hamid Reza Tohidvand , Alexis White , Ali Khosravi , Paolo Celli

Origami structures are characterized by a network of folds and vertices joining unbendable plates. For applications to mechanical design and self-folding structures, it is essential to understand the interplay between the set of folds in…

Soft Condensed Matter · Physics 2018-03-01 Bryan Gin-ge Chen , Christian D. Santangelo

The field of rigid origami concerns the folding of stiff, inelastic plates of material along crease lines that act like hinges and form a straight-line planar graph, called the crease pattern of the origami. Crease pattern vertices in the…

Metric Geometry · Mathematics 2025-07-22 Thomas C. Hull

Origami, the traditional art of paper folding, has revolutionized science and technology in recent years and has been found useful in various real-world applications. In particular, origami-inspired structures have been utilized for…

Soft Condensed Matter · Physics 2025-06-19 Rongxuan Li , Gary P. T. Choi

Origami-inspired mechanisms can transform flat sheets into functional three-dimensional dynamic structures that are lightweight, compact, and capable of complex motion. These properties make origami increasingly valuable in robotic and…

Robotics · Computer Science 2026-05-05 Tianhui Han , Shashwat Singh , Sarvesh Patil , Zeynep Temel

When a thin sheet is crushed into a small three-dimensional volume, it invariably forms a structure with a low volume fraction but high resistance to further compression. Being a far-from-equilibrium process, forced crumpling is not…

Soft Condensed Matter · Physics 2012-03-28 Anne Dominique Cambou , Narayanan Menon

Origami and crumpling are two extreme tools to shrink a 3-D shell. In the shrink/expand process, the former is reversible due to its topological mechanism, while the latter is irreversible because of its random-generated creases. We observe…

Thin sheets can be assembled into tubular origami structures that combine deployability with pronounced anisotropic stiffness, enabling applications ranging from robotics to deployable systems. However, most existing tubular origami designs…

Applied Physics · Physics 2026-04-15 Mingkai Zhang , Davood Farhadi

Origami structures have been proposed as a means of creating three-dimensional structures from the micro- to the macroscale, and as a means of fabricating mechanical metamaterials. The design of such structures requires a deep understanding…

Soft Condensed Matter · Physics 2020-04-29 M. Berry , M. E. Lee-Trimble , C. D. Santangelo

Kirigami metamaterials dramatically change their shape through a coordinated motion of nearly rigid panels and flexible slits. Here, we study a model system for mechanism-based planar kirigami featuring periodic patterns of quadrilateral…

Soft Condensed Matter · Physics 2023-06-16 Yue Zheng , Imtiar Niloy , Ian Tobasco , Paolo Celli , Paul Plucinsky

We combine large-scale atomistic modelling with continuum elastic theory to study the shapes of graphene sheets embedding nanoscale kirigami. Lattice segments are selectively removed from a flat graphene sheet and the structure is allowed…

Mesoscale and Nanoscale Physics · Physics 2015-11-06 Bastien F. Grosso , E. J. Mele
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