Condensation of elastic energy in two-dimensional packing of wire

TL;DR

This study investigates how elastic energy is distributed in a two-dimensional wire packing, revealing a hierarchical loop structure with specific fractal dimensions for energy concentration and mass distribution.

Contribution

It provides experimental measurements of elastic energy distribution and fractal dimensions in wire packing, highlighting the hierarchical nature of the structure.

Findings

Elastic energy concentrates on a set with dimension ~1.0

Mass distribution occurs on a set with dimension ~1.9

Hierarchical cascade of loops observed in the packing

Abstract

Forced packing of a long metallic wire injected into a two-dimensional cavity leads to crushed structures involving a hierarchical cascade of loops with varying curvature radii. We study the distribution of elastic energy stored in such systems from experiments, and high-resolution digital techniques. It is found that the set where the elastic energy of curvature is concentrated has dimension $D_\mathcal{S} = 1.0 \pm 0.1$, while the set where the mass is distributed, has dimension $D =1.9 \pm 0.1$.