Granular packings with sliding, rolling and twisting friction*

Intuition tells us that a rolling or spinning sphere will eventually stop due to the presence of friction. The resistance to rolling and spinning/twisting that stops one sphere also changes the microstructure of a granular packing of frictional spheres. Isostatic constraint counting allows packings of 3d spheres to span an average number of contacts per sphere between 6 to 2, depending on the types of frictional constraints. We perform discrete element modeling simulations to construct sphere packings implementing a range of frictional constraints under a stress-controlled protocol. The simulated granular packings are tested against the isostatic conjecture and are compared to experimental values. Stable packings are achievable at low volume fractions and average coordination numbers, circa 0.52 and 2.6 respectively, when the particles experience high resistance to sliding, rolling and twisting.