On the Validation of a Differential Variational Inequality Approach for the Dynamics of Granular Material

The validation of a DVI approach for the dynamics of granular material focuses on comparing the experimental and simulation results of granular flow for two tests in the Chrono::Engine simulation environment. A macro scale validation was previously carried out through examination of granular flow in PBR reactors [1]. For this work, an aluminum rig was designed and fabricated to measure the flow rate of a given amount of micro scale granular material flowing due to gravity through a slit. The flow was initiated by using a Newport UMR8.25 translational stage and Newport LTA-HL precision linear actuator to open and close the slit steadily. Once the slit was open, the weight of the granular material was transmitted to the processor via a router connected to a Cooper LFS242 Tension/Compression Cell (Serial No. 286284) and graphed over time. A model of the flow meter was created in Chrono::Engine and the results were matched to experimental runs by changing the friction coefficient between particles. After the friction coefficient of the particles was determined to be 0.15, several experimental runs with differing slit sizes were run. These flow rates were compared to the weight versus time data that Chrono::Engine output for the corresponding slit size. Runs for gap sizes of 1.5mm, 2.0mm, 2.5mm and 3.0mm were performed with 0.0624 N of granular material, which amounted to approximately 39,000 spheres with 500μm in diameter. These gap sizes corresponded to an experimental flow rate of 1.41E-2 N/s, 2.59E-2 N/s, 4.00E-2 N/s, and 4.44E-2 N/s, and a simulated flow rate of 1.40E-2 N/s, 2.62E-2 N/s, 4.05E-2 N/s, and 4.48E-2 N/s, respectively. Based on this experiment, Chrono::Engine had less than a 2% error in calculating the flow rate of the granular material through a slit. In addition to comparing flow rates, the pile repose angle from the experimental runs was compared to the simulation results. A description of the GPU execution model along with its memory spaces is provided to illustrate its potential for parallel scientific computing. The equations of motion associated with the dynamics of many rigid bodies are introduced and a solution method is presented. The solution method is designed to map well on the parallel hardware, which is demonstrated by an order of magnitude reductions in simulation time for large systems that concern the dynamics of granular material.