042905 9 arman pazouki et al physical review e 96

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ARMAN PAZOUKI et al. PHYSICAL REVIEW E 96 , 042905 (2017) TABLE VII. Summary of execution time for the standard triaxial test. Length of Average Approach time simulated (s) exec. time DEM-P settling 0 . 5 1 h 25 min DEM-P STT 1.5 4 h 55 min DEM-P total 2 . 0 6 h 20 min DEM-C settling 0 . 5 9 h 21 min DEM-C STT 1.5 44 h 14 min DEM-C total 2 . 0 53 h 35 min E. Flow sensitivity with respect to element shape A hopper experiment provides an opportunity to scrutinize via fully resolved, microscale simulation emerging macroscale attributes such as flow rate, funnel flow, arching, interlocking, jamming, etc. We reported in [ 43 ] the outcome of a DEM-C sensitivity analysis of hopper flow rate with respect to friction coefficient. The hopper, which consisted of one 45 o inclined and three vertical walls, was filled with approximately 40 000 glass disruptor beads with a 500 μ m diameter. The same hopper setup is used herein (see Figs. 13 and 14 ). The material properties for the glass beads are those from the cone penetration and PIV tests; i.e., a single value of friction coefficient μ = 0 . 7 was assumed for all contact events. Except for transitions at the onset and conclusion of the flow, we confirm the hour-glass principle that a monodisperse dry spherical-granular material flows uniformly throughout the entire process (see Table VIII ). To obtain these values, if the duration of the granular flow through hopper was T f , we split the time interval [0 . 3 , 0 . 9] T f into ten equal-size subintervals. The average flow rate for each subinterval was calculated based on a linear regression of the flow-time data in that subinterval, yielding ten flow rates. The table reports flow rate average ˙ m , standard deviation SD, and normalized standard deviation ζ = SD / ˙ m obtained using these ten values. FIG. 13. Flow of prolate ellipsoid through a hopper with α = 3 . 4. FIG. 14. Heterogeneous granular flow through a hopper. The material is composed of equal fraction of spheres, ellipsoids ( α = 2), boxes, and cylinders. The results in Table IX answer the following question: How sensitive are the simulation results to decreasing Y in order to reduce simulation times via larger integration step sizes h ? It turns out that for the hopper experiment, one can reduce Y substantially without compromising the simulation results. In our experience, the extent to which one can reduce Y is problem dependent. The DEM-P method, shown in Sec. II A to successfully capture nonlinear wave propagation, builds on the assumption that the contact scenarios encountered are of simple types such as sphere-to-sphere or sphere-to-plane contact scenarios. Then, insofar as the normal contact force is concerned, an analytical solution can be produced [ 6 , 44 46 ] in terms of quantities such as the effective radius of curvature ¯ R , effective mass ¯ m , and contact stiffness and damping parameters [see Eq. ( 2 )]. Note that these sphere-to-sphere or sphere-to-plane contact geometries, which come into play when defining, for instance, ¯ R and ¯ m , allow also for a clean tracking of the contact
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