Furrows in the wake of propagating d-cones

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.

The Complexity of Folding Self-Folding Origami

“…Recent experiments on controlled repeated crumpling and extension of sheets suggests an inability to refold along existing creases, leading to the formation of new creases [49]. While the 4-vertex patterns studied here are not good models of crumpled soft paper with significant face bending, our results do suggest that the difficulty of refolding a crease pattern, and thus the propensity to create new creases, grows with the softness of the sheet and when unfolded closer to the flat state.…”

A state variable for crumpled thin sheets

“…In elastoplastic sheets, the material scars where the localized stress exceeds the plastic yield threshold 18,19 . In this case, although defects may still migrate, they leave a furrow-like scar in their wake 20 .…”

Transition to stress focusing for locally curved sheets

“…A second outcome is the characterization of the buckling threshold. This has a practical interest for the safe handling of a piece of thin material without inducing stress focusing that would result in structural damages [13,14]. The characterization of this transition is also of interest in a context of exploiting buckling and crumpling for the realization of functional materials [15][16][17][18][19][20][21].…”