Power law scaling of lateral deformations with universal Poissons index for randomly folded thin sheets

TL;DR

This study reveals universal power law and linear behaviors in lateral deformations of folded thin sheets, highlighting differences between elastoplastic and plastic materials and their underlying fractal topologies.

Contribution

It uncovers universal deformation laws for folded sheets and links their behaviors to fractal topology, introducing a new understanding of their mechanical response.

Findings

Elastoplastic sheets follow a power law with universal Poissons index nu=0.17.

Plastic sheets exhibit a linear deformation with Poissons ratio nu_e=0.33.

Different deformation behaviors are linked to distinct fractal topologies.

Abstract

We study the lateral deformations of randomly folded elastoplastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elastoplastic sheets of paper obey a power law behavior with the universal Poissons index nu = 0.17 pm 0.01, which does not depend neither the paper kind and sheet sizes, nor the folding confinement ratio. In contrast to this, the lateral deformations of randomly folded predominantly plastic aluminum foils display the linear dependence on the axial compression with the universal Poissons ratio nu_e = 0.33 pm 0.01. This difference is consistent with the difference in fractal topology of randomly folded elastoplastic and predominantly plastic sheets, which is found to belong to different universality classes. The general form of constitutive stress-deformation relations for randomly folded elastoplastic sheets is suggested.