Bistability and equilibria of creased annular sheets and strips
arXiv:2104.09704 · doi:10.1016/j.ijsolstr.2022.111588
Abstract
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. This paper extends our recent work and is based on the following observations in tabletop models of creased disks 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.
References in corpus (25)
- Making the Cut: Lattice Kirigami Rules
- Geometric Mechanics of Curved Crease Origami
- The Geometry of Crumpled Paper
- The mechanical response of a creased sheet
- Inverse design of deployable origami structures that approximate a general surface
- "Wunderlich, meet Kirchhoff": A general and unified description of elastic ribbons and thin rods
- The designs and deformations of rigidly and flat-foldable quadrilateral mesh origami
- A non-linear rod model for folded elastic strips
- Bifurcations of buckled, clamped anisotropic rods and thin bands under lateral end translations
- Triangular buckling patterns of twisted inextensible strips
- Tension-induced multistability in inextensible helical ribbons
- Kirigami mechanics as stress relief by elastic charges
- Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable Möbius band and the attribution of the geometric problem to a variational problem"
- Overcurvature induced multistability of linked conical frusta: How a `bendy straw' holds its shape
- Plasticity and Aging of Folded Elastic Sheets
- Shape programming lines of concentrated Gaussian curvature
- Foldable Cones as a Framework for Nonrigid Origami
- Nonlinear mechanics of thin frames
- On Local Kirigami Mechanics I: Isometric Conical Solutions
- Evolving, complex topography from combining centers of Gaussian curvature
- Cutting holes in bistable folds
- On local kirigami mechanics II: Stretchable creased solutions
- Dipoles in thin sheets
- Influence of material stretchability on the equilibrium shape of a Möbius band
- Finite curved creases in infinite isometric sheets