Effect of Ridge-Ridge Interactions in Crumpled Thin Sheets

TL;DR

This study investigates how ridge-ridge interactions affect energy scaling in crumpled thin sheets using molecular dynamics simulations, revealing new scaling laws and resolving previous discrepancies between simulations and experiments.

Contribution

It introduces modified simulation protocols to analyze ridge interactions, providing new insights into energy scaling and ridge behavior in crumpled sheets.

Findings

Energy proportional to ridge length shifts from one-third to linear during crumpling.

Ridge length scales linearly with crumpled ball size R.

New scaling relation extends power-law behavior across density range.

Abstract

We study whether and how the energy scalings based on the single-ridge approximation are revised in an actual crumpled sheet; namely, in the presence of ridge-ridge interactions. Molecular Dynamics Simulation is employed for this purpose. In order to improve the data quality, modifications are introduced to the common protocol. As crumpling proceeds, we find that the average storing energy changes from being proportional to one-third of the ridge length to a linear relation, while the ratio of bending and stretching energies decreases from 5 to 2. The discrepancy between previous simulations and experiments on the material-dependence for the power-law exponent is resolved. We further determine the averaged ridge length to scale linearly with the crumpled ball size $R$, the ridge number as $1/R^2$, and the average storing energy per unit ridge length as $1/R^{2.364\sim 2.487}$. These results are consistent with the mean-field predictions. Finally, we extend the existent simulations to the high-pressure region for completeness, and verify the existence of a new scaling relation that is more general than the familiar power law at covering the whole density range.