The flexural mechanics of creased thin strips

Abstract

Many structures in Nature and Engineering are dominated by the influence of folds. A very narrow fold is a crease, which may be treated with infinitesimal width for a relatively simple geometry; commensurately, it operates as a singular hinge line with torsional elastic properties. However, real creases have a finite width and thus continuous structural properties. We therefore consider the influence of the crease geometry on the large-displacement flexural behaviour of a thin creased strip. First, we model the crease as a shallow cylindrical segment connected to initially flat side panels. We develop a theoretical model of their coupled flexural behaviour and, by adjusting the relative panel size, we capture responses from a nearly singular crease up to a full tape-spring. Precise experiments show good agreement compared to predictions.

Continuous modeling of creased annuli with tunable bistable and looping behaviors

“…In origami structures, creases have been modeled as discrete hinges ( 18 , 20 – 24 ), smooth folds with C 1 continuity ( 25 – 27 ), and as thinner ( 28 , 29 ) or narrower ( 30 ) structural elements, which either need a careful specification of matching conditions between the creases and the joining facets or require a detailed definition of the crease region. Recently, Jules et al used the Heaviside feature of a hyperbolic tangent function to describe the local geometry of creases as C ∞ continuity and studied the mechanics of creased elastica ( 31 ).…”

Bistability and equilibria of creased annular sheets and strips

“…Creases are normally modeled as rotational hinges with a finite stiffness that balances the bending moments from the thin sheets [27,46,[52][53][54]. Creases could also be modeled as continuous structures, where the local tangent makes a rapid turn within a short material length [55,56]. Accurate prediction of the mechanical responses of creased thin sheets requires incorporating both the mechanics of thin sheets and creases.…”

Compliant morphing structures from twisted bulk metallic glass ribbons

“…Here, we call these systems "compliant morphing structures". Examples of compliant structure classes are: origami, which feature axially-rigid but potentially-flexible panels connected by foldable creases [5][6][7]; kirigami, where creases are combined with cuts to expand the range of achievable morphed shapes [8][9][10]; compliant mechanism-like structures, where bulky components are connected via thin flexures [11][12][13][14][15][16][17][18]; and creaseless foldable shell structures such as tape springs and slotted cylinders [19][20][21][22]. Through careful design, some of these compliant systems achieve extreme changes of shape that are typically unattainable with other strategies.…”

“…To create compliant morphing structures made of materials relevant to structural engineering, systems that feature extremely compliant, yet robust and manufacturable hinges are needed. In recent years, ribbons (slender structural elements where length width thickness) have emerged as building blocks for morphing structures, as they can be bent and buckled [21,35,36], twisted [37][38][39][40][41][42][43][44][45] and sheared [46]. Their dimensions can be tailored to avoid the onset of plasticity when deformed.…”