Sample Size Effects on Constitutive Relations of Granular Materials—A Numerical Simulation Study with Two-Dimensional Flow of Disks

A simple shear flow of granular materials can have a range of behavior from a rate-independent plastic material to a rate-dependent viscous material. From physical experiments and computer simulations, it is known that this constitutive relation is a consequence of the shear rate, the solid concentration, and the micromechanical properties of the particles. Simple shear tests of granular materials show that in the rate-independent case, a shearing granular assembly forms crystallized regions and shearing occurs locally in a narrow band. In the rate-dependent case, these crystallized zones “melt” and the whole granular assembly participates in the shear motion. This study utilizes computer simulation to address yet another effect on the constitutive relation: the sample size. A 2D uniform disk assembly is simulated using periodic boundary conditions. Through investigating details of the kinematics the source of the transition is examined from a rate-independent to a rate-dependent fluid as the sample size increases. Results of this study have implications on the design of equipment handling granular materials. That is, rheological properties of a granular flow can change due to a change of the relative size of the equipment and the grains.