This setup shows the behavior of granular material in a vibrating box. Because of the small wall, the system can break symmetry.
Not quite a hopper, but a hole in the floor.
A very tiny simulation. 36 balls are being thrown into a container. The rolling of the particles leads to a final configuration, which is virtually flat.
The walls of the hopper are not as steep as in the other examples. The flow ends when an arch forms spontaneously and the hopper is blocked.
We have a hopper, filled with particles. Additional to the repulsive forces due to collisions we have cohesive forces. You can find more information in this publications.
A piston is compressing with a certain force onto an assembly of granular materials. No gravity is acting. The Material is very soft, so there are oscillations.
Here a sand pile is build from a line source to demonstrate the importance of static friction in sandheaps. At time step 420 the friction coefficient is quickly reduced to zero. The pile melts and the granulate flows like a liquid.
The time evolution of the force network of a sand pile which is built from a point source is shown. The width of the blue lines is proportional to the strength of the forces. The red arrows are the forces onto the ground. Note that the avalanches either go left or right and therefore lead always to slight asymmetries of the heap.
For the simulation, we have calculated the stress tensors inside the pile. In this movie, the major principal axis of the stress (crosses) and the pressure on the ground (arrows) are shown.
This heap is build using 4500 slightly elongated Particles. The first frames shows the evolution of the heap, the bottom frame shows the pressure onto the ground. You can observe the evolution of a dip below the apex of the pile