A planar rod model with flexible thin-walled cross-sections. Application to the folding of tape springs

Guinot, François; Bourgeois, Stéphane; Cochelin, Bruno; Blanchard, Laurent

doi:10.1016/j.ijsolstr.2011.09.011

Cited by 40 publications

(39 citation statements)

References 20 publications

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“…Studies on the deformation of strips with a curved [1] or folded [2] crosssection have only captured smooth deformation of the strip axis. When the cross-section of the strip consists of a sharp crease or fold, new singular bistable behaviour occurs, which is not revealed by previous models.…”

Section: Introductionmentioning

confidence: 99%

On the shape of bistable creased strips

Walker

Seffen

2018

Thin-Walled Structures

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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.

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Section: Introductionmentioning

confidence: 99%

On the shape of bistable creased strips

Walker

Seffen

2018

Thin-Walled Structures

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“…Mechanical models have been proposed to capture the large deformations of thin-walled beams. The special case of curved cross-sections must be addressed starting from the theory of shell: in this case, the bending of the centerline involves a trade-off between the shell's bending and stretching energies [26,27,28,29]. By contrast, the strip that we consider is developable; it can be studied based on an inextensible plate model, in which the stretching energy plays no role.…”

Section: Introductionmentioning

confidence: 99%

A non-linear rod model for folded elastic strips

Dias

Audoly

2014

Journal of the Mechanics and Physics of Solids

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We consider the equilibrium shapes of a thin, annular strip cut out in an elastic sheet. When a central fold is formed by creasing beyond the elastic limit, the strip has been observed to buckle out-of-plane. Starting from the theory of elastic plates, we derive a Kirchhoff rod model for the folded strip. A non-linear effective constitutive law incorporating the underlying geometrical constraints is derived, in which the angle the ridge appears as an internal degree of freedom. By contrast with traditional thin- walled beam models, this constitutive law captures large, non-rigid deformations of the cross-sections, including finite variations of the dihedral angle at the ridge. Using this effective rod theory, we identify a buckling instability that produces the out-of-plane configurations of the folded strip, and show that the strip behaves as an elastic ring having one frozen mode of curvature. In addition, we point out two novel buckling patterns: one where the centerline remains planar and the ridge angle is modulated; another one where the bending deformation is localized. These patterns are observed experimentally, explained based on stability analyses, and reproduced in simulations of the post-buckled configurations

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“…In each of these situations, regular developable solutions exist away from the defect but they are not observed as the bending energy can be progressively released by a small in-plane stretching (see also [18,19]). The stretching over large distances is also involved in the shape of drapes [20] and curtains [21], the tearing of sheets [22], or the dynamics of curved ribbons [23,24]. Our prototypal system provides a reduced model to probe these situations and the transition between smooth and singular solutions in strained sheets.…”

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confidence: 99%

How a Curved Elastic Strip Opens

et al. 2014

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An elastic strip is transversely clamped in a curved frame. The induced curvature decreases as the strip opens and connects to its flat natural shape. Various ribbon profiles are measured and the scaling law for the opening length validates a description where the in-plane stretching gradually relaxes the bending stress. An analytical model of the strip profile is proposed and a quantitative agreement is found with both experiments and simulations of the plates equations. This result provides a unique illustration of smooth nondevelopable solutions in thin sheets.

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A planar rod model with flexible thin-walled cross-sections. Application to the folding of tape springs

Cited by 40 publications

References 20 publications

On the shape of bistable creased strips

On the shape of bistable creased strips

A non-linear rod model for folded elastic strips

How a Curved Elastic Strip Opens

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