Statistical distributions in the folding of elastic structures

TL;DR

This paper investigates how elastic structures, specifically rods confined in disks, develop complex fold patterns due to competing physical effects, and proposes a statistical measure to understand their energy distribution.

Contribution

It introduces a statistical framework linking the energy distribution of rod sub-elements to the emergence of complex folding patterns in elastic structures.

Findings

Identification of a statistical measure governing energy distribution

Branches act as microscopic degrees of freedom

Foundation for a statistical mechanical theory of elastic folding

Abstract

The behaviour of elastic structures undergoing large deformations is the result of the competition between confining conditions, self-avoidance and elasticity. This combination of multiple phenomena creates a geometrical frustration that leads to complex fold patterns. By studying the case of a rod confined isotropically into a disk, we show that the emergence of the complexity is associated with a well defined underlying statistical measure that determines the energy distribution of sub-elements,``branches'', of the rod. This result suggests that branches act as the ``microscopic'' degrees of freedom laying the foundations for a statistical mechanical theory of this athermal and amorphous system.