A relaxation constant in the folding of thin viscoelastic sheets

TL;DR

This paper investigates the minimum achievable fold angle in viscoelastic sheets, revealing a universal logarithmic relaxation process linked to molecular mobility, with measured relaxation constants for Mylar and paper.

Contribution

It introduces an intrinsic relaxation constant as a new measure of material plasticity and characterizes the limits of folding in viscoelastic sheets.

Findings

Minimum fold angles are material-dependent and cannot be reduced beyond a certain point.

A universal logarithmic relaxation process occurs after deformation, independent of load or release conditions.

Measured relaxation constants are 0.01 for Mylar and 5.7 for paper.

Abstract

If one folds a thin viscoelastic sheet under an applied force, a line of plastic deformation is formed which shapes the sheet into an angle. We determine the parameters that define this angle experimentally and show that, no matter how much load one applies, it is impossible to make angles less than a certain minimum angle in a definite time. Moreover, it is shown that regardless of whether the sheet is released freely afterward or kept under the load, a logarithmic relaxation process follows the first deformation. The slope of this logarithm is the same in both conditions and depends neither on the applied force nor on the thickness of the sheet, which indicates it is directly a probe of the molecular mobility of the material. This intrinsic relaxation constant was measured 0.01 and 5.7 for Mylar and paper sheets, respectively. It is also suggested that the observed minimum angle of folding can be defined as a characteristic index for the plasticity of different materials.