Foldable cones as a framework for nonrigid origami

Andrade-Silva, Ignacio; Adda-Bedia, Mokhtar; Dias, Marcelo A.

doi:10.1103/physreve.100.033003

Cited by 21 publications

(14 citation statements)

References 31 publications

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“…This may require partitioning the deformed facet into several developable pieces with the generators bounded by different space curves [22], which is beyond the scope of this study. A recent study of the creased disk through FE modeling shows that near the crease, the lines of smallest principal curvature could intersect with the crease [63].…”

Section: Summary and Further Discussionmentioning

confidence: 99%

“…A thin sheet with a single crease is generally bistable with a second stable state obtained by locally inverting the crease, which results in a conical shape with a singularity corresponding to the vertex of the cone [28,62,63]. Elastic singularities play important roles in the mechanics of thin sheets [1,64] and are used to generate concentrated Gaussian curvatures [15,65,66].…”

Section: Introductionmentioning

confidence: 99%

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Bistability and equilibria of creased annular sheets and strips

2021

Preprint

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A creased thin disk is generally bistable since the crease could be pushed through to form a stable cone-like inverted state with an elastic singularity corresponding to the vertex of the conical surface. In a recent study, we found that this bistability could be destroyed by removing the singularity through cutting a hole around the vertex, depending on the size and shape of the hole. Particularly, to maintain the bistability, a circular hole normally cannot exceed 20% of the disk size. This paper extends our recent work and is based on the following observations in tabletop models with circular holes: (i) reducing the circumference of the creased disk by removing an annular sector could increase the hole size to be as large as the disk without destroying the bistability, (ii) with a single crease, the circular hole could be as large as the disk without loss of the bistability, and (iii) a family of stable inverted states can be obtained by inverting the disk almost anywhere along the crease. An inextensible strip model is implemented to investigate these phenomena. We formulate a minimal facet of the creased disk as a two-point boundary value problem with the creases modeled as nonlinear hinges, and use numerical continuation to conduct parametric studies. Specifically, we focus on geometric parameters which include an angle deficit that determines the circumference of the disk, the rest crease angle, the number of evenly distributed creases, and an eccentricity that determines the position of the hole on the crease. Our numerical results confirm the qualitative observations in (i)-(iii) and further reveal unexpected results caused by the coupling between these geometric parameters. Our results demonstrate that by varying the geometry of a simply creased disk, surprisingly rich nonlinear behaviors can be obtained, which shed new light on the mechanics and design of origami, kirigami, and morphable structures.

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Section: Summary and Further Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bistability and equilibria of creased annular sheets and strips

2021

Preprint

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“…The proximity of the edge of regression, or other virtual singularities living outside nominally inextensible surfaces, has been qualitatively linked to the structural stiffness response [29][30][31]. Another thread in this work is the question of multistability of systems of creases and facets with competing flexibilities, including origamic analogs of elastic singularities [32][33][34][35][36][37][38][39].…”

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confidence: 94%

“…To explore beyond the limitations of the developable model, as well as to allow independent control of rest crease angle, crease stiffness, and material thickness not possible in experiments, simulations were performed using the commercial finite element (FE) software COMSOL Multiphysics 5.4, employing quadratic shell elements, linear-elastic material, and creases introduced using a through-thickness thermal gradient [38]. These simulations also avoid self-contact effects that are an issue with experiments at small hole sizes.…”

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confidence: 99%

Cutting holes in bistable folds

Yu,

Andrade-Silva,

Dias

et al. 2020

Preprint

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A folded disk is bistable, as it can be popped through to an inverted state with elastic energy localized in a small, highly-deformed region on the fold. Cutting out this singularity relaxes the surrounding material and leads to a loss of bistability when the hole dimensions reach a critical size. These dimensions are strongly anisotropic and feature a surprising re-entrant behavior, such that removal of additional material can re-stabilize the inverted state. A model of the surface as a wide annular developable strip is found to capture the qualitative observations in experiments and simulations. These phenomena are consequential to the mechanics and design of crumpled elastic sheets, developable surfaces, origami and kirigami, and other deployable and compliant structures.

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“…Moreover, the appearance of creases in e-cones is more than a model, as it suggests an amalgamation of kirigami and origami. Indeed, the introduction of additional creases to accommodate non-rigid panel bending in origami structures is well established [33,34,35,36,37]. Such reduced-order bending models have a long history in engineering having been applied to phenomena ranging from the buckling and collapse of thin-walled structures [38,39] to the analysis of reinforced concrete slabs [40].…”

Section: Introductionmentioning

confidence: 99%

On local kirigami mechanics I: Isometric conical solutions

Sadik

Dias

2021

Journal of the Mechanics and Physics of Solids

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Following on Part I of this work series on local kirigami mechanics, we present a study of a discretely creased mechanism as a model to investigate the mechanics of the basic geometric building block of kirigami-the e-cone. We consider an annular disk with a single radial slit discritised by a series of radial creases connecting kinematically flat rigid panels. The creases allow both relative rotation and separation between panels, capturing both bending and stretching deformations. Admissible equilibrium configurations are obtained by penalising these deformations using elastic springs with stiffnesses derived from compatible continuum plate deformations. This provides a tool to study both inextensible and extensible e-cone configurations due to opening of the slit and rotation of its lips. This creased model hence offers the possibility to study the e-cone away from its isometric limit, i.e., for plates with finite thickness, and explore the full range of post-buckling (far-from-threshold) behaviour as well as initial buckling (near-threshold) instability. Our local approach provides a fundamental understanding of kirigami phenomenology, underpinned by a proper theoretical approach to geometry and mechanics.

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Foldable cones as a framework for nonrigid origami

Cited by 21 publications

References 31 publications

Bistability and equilibria of creased annular sheets and strips

Bistability and equilibria of creased annular sheets and strips

Cutting holes in bistable folds

On local kirigami mechanics I: Isometric conical solutions

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