Crumpling of a stiff tethered membrane

TL;DR

This paper introduces a numerical simulation model for crumpling of stiff tethered membranes, revealing wrinkle formation, ridge collapse, and a transition to granular-like behavior near stiffness divergence.

Contribution

The study presents a first-principles simulation capturing crumpling phenomena and links membrane ridge formation to granular force chains.

Findings

Wrinkles and ridges form during crumpling.

Scaling laws match theoretical and experimental results.

Membranes exhibit granular-like behavior near stiffness divergence.

Abstract

first-principles numerical simulation model for crumpling of a stiff tethered membrane is introduced. In our model membranes, wrinkles, ridge formation, ridge collapse, as well as the initiation of stiffness divergence, are observed. The ratio of the amplitude and wave length of the wrinkles, and the scaling exponent of the stiffness divergence, are consistent with both theory and experiment. We observe that close to the stiffness divergence there appears a crossover beyond which the elastic behavior of a tethered membrane becomes similar to that of dry granular media. This suggests that ridge formation in membranes and force-chain network formation in granular packings are different manifestations of a single phenomenon.