Cutting holes in bistable folds

Yu, T.; Andrade-Silva, I.; Dias, M. A.; Hanna, J. A.

doi:10.48550/arxiv.2008.12382

Cited by 2 publications

(5 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the original pattern, these centers deform into the tips of cones, which are point defects of Gaussian curvature. These point defects are found to play a crucial role in the mechanical behaviour of thin sheets [46,50,55]. By removing the centers, we anticipate complements will have significantly different mechanical properties, as illustrated by the comparison between the simulations in Fig.…”

Section: Interfaces In Anticones Cone-complements Orthogonal Duals An...mentioning

confidence: 85%

See 1 more Smart Citation

Interfacial metric mechanics: stitching patterns of shape change in active sheets

Feng,

Duffy,

Warner

et al. 2021

Preprint

View full text Add to dashboard Cite

Liquid crystal elastomers/glasses are active materials that can have significant metric change upon stimulation. The local metric change is determined by its director pattern that describes the ordering direction and hence the direction of contraction. We study logarithmic spiral patterns on flat sheets that evolve into cones on deformation, with Gaussian curvature localized at tips. Such surfaces, Gaussian flat except at their tips, can be combined to give compound surfaces with GC concentrated in lines. We characterize all possible metriccompatible interfaces between two spiral patterns, specifically where the same metric change occurs on each side. They are classified as hyperbolic-type, elliptic-type, concentric spiral, and continuous-director interfaces. Upon the cone deformations and additional isometries, the actuated interfaces form creases bearing non-vanishing concentrated Gaussian curvature, which is formulated analytically for all cases and simulated numerically for some examples. Analytical calculations and the simulations agree qualitatively well. Furthermore, the relaxation of Gaussian-curved creases is discussed and cantilevers with Gaussian curvature-enhanced strength are proposed. Taken together, our results provide new insights in the study of curved creases, lines bearing Gaussian curvature, and their mechanics arising in actuated liquid crystal elastomers/glasses, and other related active systems.

show abstract

Section: Interfaces In Anticones Cone-complements Orthogonal Duals An...mentioning

confidence: 85%

“…The bending energy is divergent when the surface has point defects (e.g. cone tips) [46,55]. The rest angle θ 0 (l A ) is usually treated as a constant angle in isometric origami [13,26], but is expected to vary with the arclength in the non-isometric origami case because of the concentrated GC.…”

Section: Discussionmentioning

confidence: 99%

Interfacial metric mechanics: stitching patterns of shape change in active sheets

Feng,

Duffy,

Warner

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…In addition, we assumed a constant final crease angle along the crease. Our recent work with detailed FE modelings demonstrated that the final crease angle of the inverted state usually varies along the crease [57].…”

Section: Summary and Further Discussionmentioning

confidence: 99%

“…Accurate prediction of the mechanical responses of creased thin sheets requires incorporating both the mechanics of thin sheets and creases. In flexible origami, thin sheets have been modeled as inextensible strips with the creases modeled as elastic hinges [27,57]. Various discrete models are also developed to study nonrigid origami, such as the bar and hinge model [58][59][60], triangular mesh model [14,61], and the hinge and facet model [62].…”

Section: Introductionmentioning

confidence: 99%

“…In a recent work, the author and collaborators demonstrated with both experiments and numerical continuation of an inextensible strip model that a creased thin disk could lose its bistability if the vertex of the inverted shape is cut by making a large enough hole, with the critical size dependent on the shape of the hole [57]. For example, the critical size of a circular hole is found to be less than 20% of the disk size.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bistability and equilibria of creased annular sheets and strips

2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

Cutting holes in bistable folds

Cited by 2 publications

References 48 publications

Interfacial metric mechanics: stitching patterns of shape change in active sheets

Interfacial metric mechanics: stitching patterns of shape change in active sheets

Bistability and equilibria of creased annular sheets and strips

Contact Info

Product

Resources

About