Packing transitions in the elastogranular confinement of a slender loop

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. Here, we investigate the resulting packing behaviors between a growing slender structure constrained by deformable boundaries. Experimentally, we vary the arc length of an elastic loop injected into an array of soft, spherical grains at various initial number densities. 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 ϕ_c, local re-orientations within the granular medium create an effectively curved surface leading to the emergence of a distinct circular packing morphology. These results bring new insights 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.