Optimizing packing fraction in granular media composed of overlapping spheres. Issue 4 (23rd November 2015) - Roth, Leah K.; Jaeger, Heinrich M.
Abstract : What particle shape will generate the highest packing fraction when randomly poured into a container? We use an evolutionary algorithm to discover a family of densely-packing, planar triangular shapes and verify the results in experiment with 3-D printed particles. Abstract : What particle shape will generate the highest packing fraction when randomly poured into a container? In order to explore and navigate the enormous search space efficiently, we pair molecular dynamics simulations with artificial evolution. Arbitrary particle shape is represented by a set of overlapping spheres of varying diameter, enabling us to approximate smooth surfaces with a resolution proportional to the number of spheres included. We discover a family of planar triangular particles, whose packing fraction of ϕ ∼ 0.73 is among the highest experimental results for disordered packings of frictionless particles. We investigate how ϕ depends on the arrangement of spheres comprising an individual particle and on the smoothness of the surface. We validate the simulations with experiments using 3D-printed copies of the simplest member of the family, a planar particle consisting of three overlapping spheres with identical radius. Direct experimental comparison with 3D-printed aspherical ellipsoids demonstrates that the triangular particles pack exceedingly well not only in the limit of large system size but also when confined to small containers.