On the shape of bistable creased strips

Abstract

We investigate the bistable behaviour of folded thin strips bent along their central crease. Making use of a simple Gauss mapping, we describe the kinematics of a hinge and facet model, which forms a discrete version of the bistable creased strip. The Gauss mapping technique is then generalised for an arbitrary number of hinge lines, which become the generators of a developable surface as the number becomes large. Predictions made for both the discrete model and the creased strip match experimental results well. This study will contribute to the understanding of shell damage mechanisms; bistable creased strips may also be used in novel multistable systems.

Foldable cones as a framework for nonrigid origami

“…The polar angle of the crease deviates slightly from the linear prediction for sharper folding angles. This deviation fits better the experimental results shown in reference [21], although there is still an important discrepancy from the theory because of the limits of the inextensibility hypothesis, which we explore in more detail in section IV.…”

“…In Fig. 4(c), we compare θ c (ψ) for 2 S configuration with the prediction of the linear model θ c = π/2 + 0.4386(ψ − π) [14,21]. The polar angle of the crease deviates slightly from the linear prediction for sharper folding angles.…”

“…We will refer their model as the linear model for f -cones, as it relies on the approximation of small deflections which allows to write the curvature of the surface as a linear function of the vertical component of the displacement. This system has motivated the study of other similar problems such as the bistable behavior of creased strips [21]. In this last work, the authors proposed a discrete model based on the Gauss map of several creases meeting at the vertex.…”

The flexural mechanics of creased thin strips

“…2. This is a quite different localised response: the shape of the vertex remains the same when the end rotations are increased, and it may remain in place after unloading to give bistable behaviour [9]. It is also different from opposite-sense bending of tape-springs, which produces another folded cylindrical region.…”

“…During so-called "equal-sense" bending [9] the outside edges of the strip become compressed and buckle asymmetrically, leading to twisting along the strip. Eventually the buckles coalesce into a single cylindrical fold region connected to virtually undistorted parts on both sides, see Fig.…”