Bar and hinge models for scalable analysis of origami

Filipov, Evgueni T.; Liu, Kopin; Tachi, Tomohiro; Schenk, Mark; Paulino, Gláucio H.

doi:10.1016/j.ijsolstr.2017.05.028

Cited by 215 publications

(124 citation statements)

References 49 publications

Supporting

Mentioning

119

Contrasting

Order By: Relevance

“…The total stiffness matrix K of the origami lattice is the summation of three components including the truss stretch stiffness

{boldnormalK}_{normalt} (= {boldnormalC}_{}^{normalT} {boldnormalG}_{normalt} C)

, crease torsional stiffness

{boldnormalK}_{normalc} (= {boldnormalJ}_{normalc}^{normalT} {boldnormalG}_{normalc} {boldnormalJ}_{normalc})

, and facet bending stiffness

{boldnormalK}_{normalf} (= {boldnormalJ}_{normalf}^{normalT} {boldnormalG}_{normalf} {boldnormalJ}_{normalf})

, where G t , G c , and G f are diagonal matrices containing the equivalent stiffness coefficients of the trusses, creases, and facets, respectively . The magnitudes of these stiffness coefficients need to be estimated carefully based on the facet geometries and constituent material properties . It is worth emphasizing that the lattice formulation discussed above is only suitable for analyzing small deformations.…”

Section: Analytical Tools For Origami Mechanicsmentioning

confidence: 99%

Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties

et al. 2018

View full text Add to dashboard Cite

devices, [26,27] to small-scale nano- [28][29][30] and DNA origamis. [31] A common theme in these studies is to exploit the sophisticated shape transformations from folding. For example, an origami robot is typically fabricated in a 2D flat configuration and then folded into the prescribed 3D shape to perform its tasks. The origamis have been treated essentially as linkage mechanisms in which rigid facets rotate around hingelike creases (aka "rigid-folding origami"). Elastic deformation of the constituent sheet materials or the dynamics of folding are often neglected. Such a limitation in scope indeed resonates the origin of this field, that is, folding was initially considered as a topic in geometry and kinematics.However, the increasingly diverse applications of origami require us to understand the force-deformation relationship and other mechanical properties of folded structures. Over the last decade, studies in this field started to expand beyond design and kinematics and into the domain of mechanics and dynamics. Catalyzed by this development, a family of architected origami materials quickly emerged (Figure 1). These materials are essentially assemblies of origami sheets or modules with carefully designed crease patterns. The kinematics of folding still plays an important role in creating certain properties of these origami materials. For example, rigid folding of the classical Miura-ori sheet induces an in-plane deformation pattern with auxetic properties (aka negative Poisson's ratios). [32,33] However, elastic energy in the deformed facets and creases, combined with their intricate spatial distributions, impart the origami materials with a rich list of desirable and even unorthodox properties that were never examined in origami before. For example, the Ron-Resch fold creates a unique tri-fold structure where pairs of triangular facets are oriented vertically to the overall origami sheet and pressed against each other. Such an arrangement can effectively resist buckling and create very high compressive load bearing capacity. [34] Other achieved properties include shape-reconfiguration, tunable nonlinear stiffness and dynamic characteristics, multistability, and impact absorption.Since the architected origami materials obtain their unique properties from the 3D geometries of the constituent sheets or modules, they can be considered a subset of architected cellular solids or mechanical metamaterials. [35][36][37][38][39] However, the origami materials have many unique characteristics. The rich geometries of origami offer us great freedom to tailor targeted 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 geomet...

show abstract

“…The total stiffness matrix K of the origami lattice is the summation of three components including the truss stretch stiffness

{boldnormalK}_{normalt} (= {boldnormalC}_{}^{normalT} {boldnormalG}_{normalt} C)

, crease torsional stiffness

{boldnormalK}_{normalc} (= {boldnormalJ}_{normalc}^{normalT} {boldnormalG}_{normalc} {boldnormalJ}_{normalc})

, and facet bending stiffness

{boldnormalK}_{normalf} (= {boldnormalJ}_{normalf}^{normalT} {boldnormalG}_{normalf} {boldnormalJ}_{normalf})

Section: Analytical Tools For Origami Mechanicsmentioning

confidence: 99%

Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties

et al. 2018

View full text Add to dashboard Cite

show abstract

“…This feature is demonstrated through a structural analysis of a tube using the finite element method. The model had identical n = 6, Figure 3(a), and the facets were set to be 2 orders stiffer than the creases to distinguish the deformation of these two components [31][32][33] (supplementary material, S4). The simulation started from θ = 130°n ear configurations III R and terminated at θ = 88°just beyond configuration III L .…”

Section: Mechanism-structure-mechanism Transitionmentioning

confidence: 99%

Folding of Tubular Waterbomb

Feng

Chen

et al. 2020

Research

View full text Add to dashboard Cite

Origami has recently emerged as a promising building block of mechanical metamaterials because it offers a purely geometric design approach independent of scale and constituent material. The folding mechanics of origami-inspired metamaterials, i.e., whether the deformation involves only rotation of crease lines (rigid origami) or both crease rotation and facet distortion (nonrigid origami), is critical for fine-tuning their mechanical properties yet very difficult to determine for origami patterns with complex behaviors. Here, we characterize the folding of tubular waterbomb using a combined kinematic and structural analysis. We for the first time uncover that a waterbomb tube can undergo a mixed mode involving both rigid origami motion and nonrigid structural deformation, and the transition between them can lead to a substantial change in the stiffness. Furthermore, we derive theoretically the range of geometric parameters for the transition to occur, which paves the road to program the mechanical properties of the waterbomb pattern. We expect that such analysis and design approach will be applicable to more general origami patterns to create innovative programmable metamaterials, serving for a wide range of applications including aerospace systems, soft robotics, morphing structures, and medical devices.

show abstract

“…Admittedly, finite element analysis is computationally expensive. Recently, some researchers have proposed simple and efficient pin-jointed models [60] or bar-hinge models [62,63] to analyze the deformation behavior of origami structures. Chen and Feng [60] simulated the Miura origami structures by pin-jointed structures and verified rigid folding behavior of such kind of structures from the very small strains of the members.…”

Section: Large Deformations Of Origami Structuresmentioning

confidence: 99%

Geometric and Kinematic Analyses and Novel Characteristics of Origami-Inspired Structures

2019

View full text Add to dashboard Cite

In recent years, origami structures have been gradually applied in aerospace, flexible electronics, biomedicine, robotics, and other fields. Origami can be folded from two-dimensional configurations into certain three-dimensional structures without cutting and stretching. This study first introduces basic concepts and applications of origami, and outlines the common crease patterns, whereas the design of crease patterns is focused. Through kinematic analysis and verification on origami structures, origami can be adapted for practical engineering. The novel characteristics of origami structures promote the development of self-folding robots, biomedical devices, and energy absorption members. We briefly describe the development of origami kinematics and the applications of origami characteristics in various fields. Finally, based on the current research progress of crease pattern design, kinematic analysis, and origami characteristics, research directions of origami-inspired structures are discussed.

show abstract

Bar and hinge models for scalable analysis of origami

Cited by 215 publications

References 49 publications

Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties

Architected Origami Materials: How Folding Creates Sophisticated Mechanical Properties

Folding of Tubular Waterbomb

Geometric and Kinematic Analyses and Novel Characteristics of Origami-Inspired Structures

Contact Info

Product

Resources

About