Yielding, rigidity, and tensile stress in sheared columns of hexapod granules

Abstract

Granular packings of nonconvex or elongated particles can form freestanding structures like walls or arches. For some particle shapes, such as staples, the rigidity arises from interlocking of pairs of particles, but the origins of rigidity for noninterlocking particles remains unclear. We report on experiments and numerical simulations of sheared columns of "hexapods," particles consisting of three mutually orthogonal sphero-cylinders whose centers coincide. We vary the length-to-diameter aspect ratio, α, of the sphero-cylinders and subject the packings to quasistatic direct shear. For small α, we observe a finite yield stress. For large α, however, the column becomes rigid when sheared, supporting stresses that increase sharply with increasing strain. Analysis of x-ray microcomputed tomography (micro-CT) data collected during the shear reveals that the stiffening is associated with a tilted, oblate cluster of hexapods near the nominal shear plane in which particle deformation and average contact number both increase. Simulation results show that the particles are collectively under tension along one direction, even though they do not interlock pairwise. These tensions comes from contact forces carrying large torques, and they are perpendicular to the compressive stresses in the packing. They counteract the tendency to dilate, thus stabilizing the particle cluster.

Link between packing morphology and the distribution of contact forces and stresses in packings of highly nonconvex particles

“…An exception is made for the particle aspect ratio [defined as the ratio of the overall length of a particle L to the diameter of the protruding arms d p (Fig. 3)] which was used by other works [21,22] to describe star-shaped particles. To aid the comparison between our work and the works reported in Refs.…”

“…To aid the comparison between our work and the works reported in Refs. [21,22] the relationship between the particle aspect ratio and the particle sphericity is given in the Supplemental Material [43].…”

On regular and random two-dimensional packing of crosses

“…Besides spheres, other particle shapes as for example ellipsoids [7], polyhedra [8][9][10][11][12] or spherocylinders [13] have attracted the interest of researchers. Studies on packing problems in 3D included also non-convex particles like stars or hexapods [14][15][16]. The practical relevance of the latter type of objects may be found in construction industry and architecture [17,18], when one is looking for a material that forms stable aggregates of a desired shape, but on the other hand can be disassembled again with little efforts for a structural redesign.…”

Stress propagation in locally loaded packings of disks and pentagons

“…In the past two decades, advances in technologies that can mass-produce grains of well defined shapes (e.g., 3D printing 17,18 and laser cutting 19 ) and computational tools that can efficiently model aspherical grains [20][21][22][23] have enabled numerous studies of granular materials with nonspherical grains. Many studies have characterized the mechanics and dynamics of elongated grains, such as plates or rods with varying aspect ratio [24][25][26][27][28][29][30][31][32][33][34][35][36][37] ; grains with concavities, such as staple-like grains or hexapods 17,18,[38][39][40][41] ; and angular grains, such as tetrahedra or pentagons 17,18,23,33,[42][43][44][45][46] .…”

“…Grain-scale interactions between nonspherical grains can differ significantly from the interactions that can arise between spherical grains. For instance, the presence of flat edges or significant elongation of grains introduces rotational resistance for individual grains experiencing force-bearing edge-edge (or faceface) contacts 23,[42][43][44]46,47 , and concave particles can interlock and support tensile stresses 39,40 . Microscopic interactions associated with various grain shapes have been shown to influence macroscopic properties of granular materials in many contexts, including the shear strength 13,17,18,39,43 and structural characteristics of jammed packings 23,26,28,30,30,33,35,36,44,[48][49][50][51][52][53][54][55][56] , the dynamical organization of anisotropic grains in driven granular media 27,29,31,37,57 , the rheology of dense granular flows 19,58 , the flow and clogging dynamics of granular materials driven through restricted apertures 27,34,[59][60][61] , ...…”