Topological crossovers in the forced folding of self-avoiding matter

TL;DR

This paper investigates the scaling laws governing the topological transitions in forced folding of elastic and plastic thin materials, revealing experimental observations of crossovers from 3D to 2D and 1D structures.

Contribution

It derives scaling relations for topological crossovers in forced folding and experimentally observes these in plastic aluminum strips, highlighting the influence of material properties.

Findings

Identified topological crossovers from 3D to 2D and 1D folding.

Observed plastic aluminum strips exhibit these crossovers.

Fractal dimension of folded sheets depends on thickness due to strain relaxation.

Abstract

We study the scaling properties of forced folding of thin materials of different geometry. The scaling relations implying the topological crossovers from the folding of threedimensional plates to the folding of two-dimensional sheets, and further to the packing of one-dimensional strings, are derived for elastic and plastic manifolds. These topological crossovers in the folding of plastic manifolds were observed in experiments with predominantly plastic aluminum strips of different geometry. Elasto-plastic materials, such as paper sheets during the (fast) folding under increasing confinement force, are expected to obey the scaling force-diameter relation derived for elastic manifolds. However, in experiments with paper strips of different geometry, we observed the crossover from packing of one-dimensional strings to folding two dimensional sheets only, because the fractal dimension of the set of folded elasto-plastic sheets is the thickness dependent due to the strain relaxation after a confinement force is withdrawn.