Furrows in the wake of propagating d-cones.

Omer Gottesman,Efi Efrati,Shmuel M Rubinstein

doi:10.1038/ncomms8232

Omer Gottesman, Efi Efrati + Show 1 more

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https://doi.org/10.1038/ncomms8232

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Abstract

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.

Highlights

A crumpled sheet of paper displays an intricate pattern of creases and point-like singular structures, termed d-cones
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]
For purely elastic sheets, point defects and their connecting ridges continuously respond to loading by the redistribution of the elastic energy through defect migration[20], analogous to the role played by dislocations in an ordered solid

Summary

Introduction

A crumpled sheet of paper displays an intricate pattern of creases and point-like singular structures, termed d-cones. To better understand this new type of creases, which are inherently plastic and are formed by the propagation of single point defects, we create and manipulate them in isolation. The force required to propagate the singularity and elongate the furrow scales quadratically with the thickness of the sheet

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