Constant Torque Rolling Resistance Makes Shear Friction Depend on the Time Step Rather than on Particle Stiffness in Ring Shear Simulations of Monodisperse Glass Spheres

Discrete element models of glass beads are routinely run with particles two to three orders of magnitude softer than real glass, and softened models usually show lower shear strength, attributed to the added contact compliance. Softening, however, also lengthens the time step allowed by the Rayleigh criterion, so compliance and time step change together. We sheared monodisperse glass spheres with a constant torque rolling resistance in a ring shear cell at 10 kPa, varied the ratio of shear modulus to normal stress G/σn from 103 to 3 × 105, and separated the two effects by restarting runs at 103, 104 and 105 with time steps up to eight times smaller. With Rayleigh-based steps, the friction of the softest grains was 21% below that of the stiffest; at reduced steps, it differed by no more than about 2% across the range, and without rolling resistance it depended on neither quantity. The friction deficit grows with the angular impulse that the rolling torque imparts in one step, which also produces spurious spin fluctuations. Coordination number, rattler fraction and contact persistence, by contrast, change with the stiffness itself. When constant torque rolling resistance is used, time step convergence must therefore be checked separately from stiffness.