Discrete Element Modeling of Complex Granular Flows
Granular materials occur almost everywhere in nature, and are actively studied in many fields of research, from food industry to planetary science. One approach to the study of granular media, the continuum approach, attempts to find a constitutive law that determines the material’s flow, or strain, under applied stress. The main difficulty with this approach is that granular systems exhibit different behavior under different conditions, behaving at times as an elastic solid (e.g. pile of sand), at times as a viscous fluid (e.g. when poured), or even as a gas (e.g. when shaken). Even if all these physics are accounted for, numerical implementation is made difficult by the wide and often discontinuous ranges in continuum density and sound speed. A different approach is Discrete Element Modeling (DEM). Here the goal is to directly model every grain in the system as a rigid body subject to various body and surface forces. The advantage of this method is that it treats all of the above regimes in the same way, and can easily deal with a system moving back and forth between regimes. But as a granular system typically contains a multitude of individual grains, the direct integration of the system can be very computationally expensive.
For this reason most DEM codes are limited to spherical grains of uniform size. However, spherical grains often cannot replicate the behavior of real world granular systems. A simple pile of spherical grains, for example, relies on static friction alone to keep its shape, while in reality a pile of irregular grains can maintain a much steeper angle by interlocking force chains. In the present study we employ a commercial DEM, nVidia’s PhysX Engine, originally designed for the game and animation industry, to simulate complex granular flows with irregular, non-spherical grains. This engine runs as a multi threaded process and can be GPU accelerated.
We demonstrate the code’s ability to physically model granular materials in the three regimes mentioned above: (1) a static and steep granular pile; (2) granular flow with a complex velocity field; and (3) an agitated granular pile resulting in size based segregation. We compare our simulations to laboratory experiments in the first and third regimes, and to a known empirical constitutive law (Jop et al. 2006) in the second. We discuss application of this code in studies of several planetary systems, including analysis of the tensile strength of comets from evidence of tidal disruption, and bulking and banding on rubble-pile asteroids, as an indication of their seismic history.
Keywords: COMPUTATIONAL GEOPHYSICS, Numerical solutions