Packing Transitions in the Elastogranular Confinement of a Slender Loop

TL;DR

This study explores how a slender elastic loop packs within a deformable granular medium, revealing a transition from flat to circular packing morphologies as initial packing density increases, with implications for biological and engineering systems.

Contribution

It introduces a novel experimental framework to analyze packing transitions of elastic loops in deformable granular media, highlighting a critical density-driven morphological change.

Findings

Below critical density, loops fold against a flat surface.

Above critical density, loops form circular packings due to local re-orientations.

Results inform understanding of biological and robotic packing strategies.

Abstract

Confined thin structures are ubiquitous in nature. Spatial and length constraints have led to a number of novel packing strategies at both the micro-scale, as when DNA packages inside a capsid, and the macro-scale, seen in plant root development and the arrangement of the human intestinal tract. By varying the arc length of an elastic loop injected into an array of monodisperse, soft, spherical grains at varying initial number density, we investigate the resulting packing behaviors between a growing slender structure constrained by deformable boundaries. At low initial packing fractions, the elastic loop deforms as though it were hitting a flat surface by periodically folding into the array. Above a critical packing fraction $\phi_c$, local re-orientations within the granular medium create an effectively curved surface leading to the emergence of a distinct circular packing morphology in the adjacent elastic structure. These results will bring new insight into the packing behavior of wires and thin sheets and will be relevant to modeling plant root morphogenesis, burrowing and locomotive strategies of vertebrates & invertebrates, and developing smart, steerable needles.