The relation between ridges and crumples

Crumpling is the name given to the structure created when a thin sheet has been forced to occupy a volume much smaller than the sheet’s largest dimension. Crumples strongly resist compression, making them an interesting lightweight material. How a crumple resists compression is a challenging question to answer, though recently we have proposed an empirical relation which applies to both elastic and plastic sheets. Here we examine different ‘building block’ structures for clues as to the origin of the empirical force law. Specifically, we focus on the stretching ridge which joins two developable-cones and has long been hypothesized to be responsible for the crumple’s strength. We show that elastic and plastic ridges, though geometrically identical when formed, behave very differently under compression. The elastic ridge smoothly collapses annihilating one d-cone in the process, whereas the plastic material allows no motion of the d-cone cores, building stress until buckling. Remarkably, before failure the plastic and elastic ridges can be fit by the same empirical model as can the crumple itself. We discuss the curious relationship.