Tensional twist-folding of sheets into multilayered architectures and scrolled yarns (original) (raw)
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Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties
Advanced Materials, 2018
Origami, the ancient Japanese art of paper folding, is not only an inspiring technique to create sophisticated shapes, but also a surprisingly powerful method to induce nonlinear mechanical properties. Over the last decade, advances in crease design, mechanics modeling, and scalable fabrication have fostered the rapid emergence of architected origami materials. These materials typically consist of folded origami sheets or modules with intricate 3D geometries, and feature many unique and desirable material properties like auxetics, tunable nonlinear stiffness, multistability, and impact absorption. Rich designs in origami offer great freedom to design the performance of such origami materials, and folding offers a unique opportunity to efficiently fabricate these materials at vastly different sizes. Here, recent studies on the different aspects of origami materials—geometric design, mechanics analysis, achieved properties, and fabrication techniques—are highlighted and the challenges...
Mechanics of paper-folded origami: A cautionary tale
Mechanics Research Communications, 2020
Folded paper has a long history in origami artwork and is used by engineers to rapidly prototype designs of adaptive structures and mechanical metamaterials. However, engineers should be cautious when using paper to investigate the mechanical properties of origami structures. We show that the nonlinear, pseudo-plastic behaviour of paper folds complicates the modelling of the mechanical properties of an origami structure. However, this pseudo-plastic behaviour could also present a new design space to tailor the mechanical properties of origami by controlling the rest angles of the folds.
Self-organized rod undulations on pre-stretched textiles
Bioinspiration & Biomimetics, 2022
Textile technology is a traditional approach to additive manufacturing based on one-dimensional yarn. Printing solid rods onto pre-stretched textiles creates internal stresses upon relaxation of the pre-stretch, which leads to buckling-induced out-of-plane deformation of the textile. Similar behaviours are well known to occur also in biological systems where differential growth leads to internal stresses that are responsible for the folding or wrinkling of leaves, for example. Our goal was to get a quantitative understanding of this wrinkling by a systematic experimental and numerical investigation of parallel rods printed onto a pre-stretched textile. We vary rod thickness and spacing to obtain wavelength and phase coherence of the wrinkles as a function of these parameters. We also derive a simple analytical description to rationalize these observations. The result is a simple analytical estimate for the phase diagram of behaviours that may be used for design purposes or to describe wrinkling phenomena in biological or bioinspired systems.
International Journal of Mechanical Sciences, 2021
Using non-rigid-foldable origami patterns to design mechanical metamaterials could potentially offer more versatile behaviors than the rigid-foldable ones, but their applications are limited by the lack of analytical framework for predicting their behavior. Here, we propose a theoretical model to characterize a non-rigid-foldable square-twist origami pattern by its rigid origami counterpart. Based on the experimentally observed deformation mode the square-twist, a virtual crease was added in the central square to turn the non-rigid-foldable pattern to a rigid-foldable one. Two possible deformation paths of the non-rigid-foldable pattern were calculated through kinematic analysis of its rigid origami counterpart, and the associated energy and force were derived analytically. Using the theoretical model, we for the first time discovered that the non-rigid-foldable structure bifurcated to follow a low-energy deformation path, which was validated through experiments. Furthermore, the mechanical properties of the structure could be programmed by the geometrical parameters of the pattern and material stiffness of the creases and facets. This work thus paves the way for development of non-rigid-foldable origami-based metamaterials serving for mechanical, thermal, and other engineering applications.
Auxetic deformation of the weft-knitted Miura-ori fold
Textile Research Journal, 2019
Negative Poisson's ratio (NPR) material with unique geometry is rare in nature and has an auxetic response under strain in a specific direction. With this unique property, this type of material is significantly promising in many specific application fields. The curling structure commonly exists in knitted products due to the unbalanced force inside a knit loop. Thus, knitted fabric is an ideal candidate to mimic natural NPR materials, since it possesses such an inherent curly configuration and the flexibility to design and process. In this work, a weft-knitted Miura-ori fold (WMF) fabric was produced that creates a self-folding three-dimensional structure with NPR performance. Also, a finite element analysis model was developed to simulate the structural auxetic response to understand the deformation mechanism of hierarchical thread-based auxetic fabrics. The simulated strain-force curves of four WMF fabrics quantitatively agree with our experimental results. The auxetic morphologies, Poisson's ratio and damping capacity were discussed, revealing the deformation mechanism of the WMF fabrics. This study thus provides a fundamental framework for mechanicalstimulating textiles. The developed NPR knitted fabrics have a high potential to be employed in areas of tissue engineering, such as artificial blood vessels and artificial folding mucosa.
The shape and mechanics of curved-fold origami structures
EPL (Europhysics Letters), 2012
PACS 46.70.-p-Application of continuum mechanics to structures PACS 46.32.+x-Static buckling and instability PACS 02.40.Hw-Classical differential geometry Abstract-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 fold prescribes the shape of the entire origami structure. To better explore these structures, we derive continuum equations, valid in the limit of vanishing spacing between folds, to describe the smooth surface intersecting all the mountain folds. We find that this surface has negative Gaussian curvature with magnitude equal to the square of the fold's torsion. A series of open folds with constant fold angle generate a helicoid.
Curving origami with mechanical frustration
Extreme Mechanics Letters, 2021
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 imprinted crease network does not exhibit a geodesic curvature, the emergent structure is characterized by an effective curvature produced by the deformed central fold. Moreover, both finite element analysis and manually made mylar origamis show a robust empirical relation between the imprinted crease network's dimensions and the apparent curvature. A detailed examination of this geometrical relation shows the existence of three typical elastic deformations, which in turn induce three distinct types of morphogenesis. We characterize the corresponding kinematics of crease network deformations and determine their phase diagram. Taking advantage of the frustration caused by the competition between crease stiffness and kinematics of crease network deformations, we provide a novel tool for designing curved origami structures constrained by strong geometrical properties.
Geometric Mechanics of Curved Crease Origami
Physical Review Letters, 2012
Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations which allow us to generalize our analysis to study structures with multiple curved creases.
Mechanical response of fabric sheets to three-dimensional bending, twisting, and stretching
Acta Mechanica Sinica, 2015
A model for the mechanics of woven fabrics is developed in the framework of two-dimensional elastic surface theory. Thickness effects are modeled indirectly in terms of appropriate constitutive equations. The model accounts for the strain of the fabric and additional effects associated with the normal bending, geodesic bending, and twisting of the constituent fibers.
Origami engineering: Creating dynamic functional materials through folded structures
Hybrid Advances, 2023
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