Experimental Study of Developable Cones

Chaı̈eb, Sahraoui; Melo, Francisco; Géminard, Jean‐Christophe

doi:10.1103/physrevlett.80.2354

Cited by 85 publications

(85 citation statements)

References 17 publications

(16 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In many cases, however, the prescribed boundary conditions allow no such stretch-free configuration with finite bending energy; such is the case when a thin sheet is confined to a small volume 10 . In this case the unavoidable in-plane stretching localizes to point-like and line-like structures termed d-cones and stretching ridges, respectively 1,3,8,[11][12][13][14] . It is believed that the crumpled configuration of a highly confined thin sheet can be fully described using only these two deformation modes.…”

mentioning

confidence: 99%

Furrows in the wake of propagating d-cones

2015

View full text Add to dashboard Cite

A crumpled sheet of paper displays an intricate pattern of creases and point-like singular structures, termed d-cones. It is typically assumed that elongated creases form when ridges connecting two d-cones fold beyond the material yielding threshold, and scarring is thus a by-product of the folding dynamics that seek to minimize elastic energy. Here we show that rather than merely being the consequence of folding, plasticity can act as its instigator. We introduce and characterize a different type of crease that is inherently plastic and is formed by the propagation of a single point defect. When a pre-existing d-cone is strained beyond a certain threshold, the singular structure at its apex sharpens abruptly. The resulting focusing of strains yields the material just ahead of the singularity, allowing it to propagate, leaving a furrow-like scar in its wake. We suggest an intuitive fracture analogue to explain the creation of furrows.

show abstract

mentioning

confidence: 99%

Furrows in the wake of propagating d-cones

2015

View full text Add to dashboard Cite

show abstract

“…This is evident in a sheet of paper for example, which is soft to bending deformations but highly resistant to stretching [1]. Even under significant deformation, thin elastic structures tend to concentrate their stretching distortion into small regions of high strain surrounded by bent but relatively unstretched regions [2][3][4][5][6]. Because of this, isometriesdeformations that deform a surface without stretchingplay a privileged role in the mechanics of thin shells.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear mechanics of rigidifying curves

Mosleh¹,

Santangelo²

2017

Phys. Rev. E

View full text Add to dashboard Cite

Thin shells are characterized by a high cost of stretching compared to bending. As a result isometries of the midsurface of a shell play a crucial role in their mechanics. In turn, curves on the midsurface with zero normal curvature play a critical role in determining the number and behavior of isometries. In this paper, we show how the presence of these curves results in a decrease in the number of linear isometries. Paradoxically, shells are also known to continuously fold more easily across these rigidifying curves than other curves on the surface. We show how including nonlinearities in the strain can explain these phenomena and demonstrate folding isometries with explicit solutions to the nonlinear isometry equations. In addition to explicit solutions, exact geometric arguments are given to validate and guide our analysis in a coordinate-free way.

show abstract

“…Scaling laws governing the energy and size of the ridge have been obtained analytically and tested numerically [2][3][4][5]. Point-like singularities are also studied extensively [1,[6][7][8][9][10][11][12]. Besides the understanding of these singularities, however, there is a lack of knowledge about the geometrical and mechanical effects of confining forces on a thin elastic sheet.…”

Section: Introductionmentioning

confidence: 99%

Spontaneous curvature cancellation in forced thin sheets

Tao

Witten

2006

Phys. Rev. E

View full text Add to dashboard Cite

In this paper we report numerically observed spontaneous vanishing of mean curvature on a developable cone made by pushing a thin elastic sheet into a circular container [1]. We show that this feature is independent of thickness of the sheet, the supporting radius and the amount of deflection. Several variants of developable cone are studied to examine the necessary conditions that lead to the vanishing of mean curvature. It is found that the presence of appropriate amount of radial stress is necessary. The developable cone geometry somehow produces the right amount of radial stress to induce just enough radial curvature to cancel the conical azimuthal curvature. In addition, the circular symmetry of supporting container edge plays an important role. With an elliptical supporting edge, the radial curvature overcompensates the azimuthal curvature near the minor axis and undercompensates near the major axis. Our numerical finding is verified by a crude experiment using a reflective plastic sheet. We expect this finding to have broad importance in describing the general geometrical properties of forced crumpling of thin sheets.

show abstract

Experimental Study of Developable Cones

Cited by 85 publications

References 17 publications

Furrows in the wake of propagating d-cones

Furrows in the wake of propagating d-cones

Nonlinear mechanics of rigidifying curves

Spontaneous curvature cancellation in forced thin sheets

Contact Info

Product

Resources

About