Elastogranular Mechanics: Buckling, Jamming, and Structure Formation

Abstract

Confinement of a slender body into a granular array induces stress localization in the geometrically nonlinear structure, and jamming, reordering, and vertical dislodging of the surrounding granular medium. By varying the initial packing density of grains and the length of a confined elastica, we identify the critical length necessary to induce jamming, and demonstrate how folds couple with the granular medium to localize along grain boundaries. Above the jamming threshold, the characteristic length of elastica deformation is shown to diverge in a manner that is coupled with the motion and rearrangement of the grains, suggesting the ordering of the granular array governs the deformation of the slender structure. However, overconfinement of the elastica will vertically dislodge grains, a form of stress relaxation in the granular medium that illustrates the intricate coupling in elastogranular interactions.

Bending transition in the penetration of a flexible intruder in a two-dimensional dense granular medium

“…In contrast with two recent works focusing on buckling [34,35], the present study will highlight a bending transition of the flexible intruder and an associated transition in the structure of the granular medium.…”

“…This critical length can be viewed as an elasto-granular length as also defined in [35] in analogy with other works on elasto-capillary phenomena [3]. The stability of the flexible beam thus appears to be controlled by two parameters: the rigidity (here the length) and the packing fraction of the granular medium.…”

“…The high sensitivity of flexible intruders to low forces opens here a promising new way of probing the mechanical behavior of granular media [34][35][36]. The complexity of such a question of elastogranular mechanics (as recently coined in Ref.…”

Elastogranularity in binary granular mixtures

“…In contrast to the situation below jamming, the behavior of packings prepared above φ j tends to be dictated by the highly dense granular array [27]. In the monodisperse case, the elastica is seen to localize deformations within a diamond-shaped "lozange" region, the boundary contour of which is set by the tendency of the grains towards hexagonal packing, and the length of which is governed by a characteristic granular length scale λ c , reflecting the extent to which forces originating with the thin structure may diffuse out into the medium [27]. In these configurations the elastica is kinematically frustrated.…”

“…(See videos S2, S3 and the Supplemental Material in Ref. [27] for movies of these compression tests). From these experiments, we find φ j = {0.8305 ± 0.0135, 0.8277 ± 0.0134, 0.7950 ± 0.0110} for η = [1.0, 1.2, 1.9], respectively.…”