Research in the Matuttis Group

Granular materials and friction

Computational fluid dynamics and granular particles in fluids fluid

2D-movies on this page by Alexander Schinner https://scholar.google.com/citations?user=9lg6jfUAAAAJ&hl=de

Granular materials in motion may look like fluids, but as fluids go, they are pretty strange ones: Unlike the flow of Newtonian Fluids, where the upper surface of the fluid tries to stay horizontal, and the flow is determined by the viscosity and flow velocity, the flow of granular materials depends on the boundaries around the materials.

If the vessel is a narrowing hopper, all the grains will be in motion, like a fluid, which is called mass low. This is actually a problem in silo engineering, because in a silo with 50 tons of materials, all 50 tons are moving, and stopping the outflow will stop the 50 tons all at once - with considerable strain on the mechanic structure of the silo.

If grains flow through a hole in a horizontal bottom, there is only a narrow region where the particles drop downwards, and at the end, slopes towards the left and the right will be left over. In the case of a hopper, these dead zones of the flow mean that the hopper will never empty completely.

Granular Dynamics and friction

An important feature of granular dynamics is friction: Without friction, granular dynamics is not realistic. In the following, a heap is built up on a frictional floor, with the same coefficient of friction between the particles and the particles with the floor up to frame 400 with friction in the simulation. At frame number 400, the friction is switched off. The heap disintegrates and flows out like a fluid towards the sidewalls, forming a horizontal surface. (It is not a Newtonian fluid like water, because it can compensate normal stresses, but this "granular fluid" cannot form heaps.)

In other words, when we have stresses forming inside the heap, the friction locks the particles onto each other and the stress distribution (and the maintenance of the heap) depends crucially on the friction between the particles.

Here is another heap formation with friction, but instead of the particles, the forces between the particles are drawn as blue lines, with the line thickness proportional to the forces. On the floor, the stresses are averaged over a representative volume and the largest stress component is drawn as red arrow:

This is an example with clogging in a hopper, where the particles are large enough and the static friction is strong enough so that the hopper cloggs.

Granular dynamics, and modeling non-spherical grains

One of the most crucial properties of dry granular materials is that they form heaps: Poured out from a
vessel, they automatically form a layered structure with a peak somewhere close to the middle.

Necessary for this is shape: The dynamics of granular particles is governed by a competition of rolling and sliding. Spheres have not need to slide, they can roll with minimum resistance, and with pure rolling, heaps can and will disintegrate to single layers.

In our research, we model granular particles as polytopes (polygons in two dimensions, polyhedra in three dimensions) with friction, to obtain granular dynamics which is as realistic as possible:

Granular materials in motion may look like fluids, but as fluids go, they are pretty strange ones: Unlike the flow of Newtonian Fluids, where the upper surface of the fluid tries to stay horizontal, and the flow is determined by the viscosity and flow velocity, the flow of granular materials depends on the boundaries around the materials.
	If the vessel is a narrowing hopper, all the grains will be in motion, like a fluid, which is called mass low. This is actually a problem in silo engineering, because in a silo with 50 tons of materials, all 50 tons are moving, and stopping the outflow will stop the 50 tons all at once - with considerable strain on the mechanic structure of the silo.
	If grains flow through a hole in a horizontal bottom, there is only a narrow region where the particles drop downwards, and at the end, slopes towards the left and the right will be left over. In the case of a hopper, these dead zones of the flow mean that the hopper will never empty completely.

Granular Dynamics and friction An important feature of granular dynamics is friction: Without friction, granular dynamics is not realistic. In the following, a heap is built up on a frictional floor, with the same coefficient of friction between the particles and the particles with the floor up to frame 400 with friction in the simulation. At frame number 400, the friction is switched off. The heap disintegrates and flows out like a fluid towards the sidewalls, forming a horizontal surface. (It is not a Newtonian fluid like water, because it can compensate normal stresses, but this "granular fluid" cannot form heaps.)

In other words, when we have stresses forming inside the heap, the friction locks the particles onto each other and the stress distribution (and the maintenance of the heap) depends crucially on the friction between the particles. Here is another heap formation with friction, but instead of the particles, the forces between the particles are drawn as blue lines, with the line thickness proportional to the forces. On the floor, the stresses are averaged over a representative volume and the largest stress component is drawn as red arrow:

Granular dynamics, and modeling non-spherical grains
One of the most crucial properties of dry granular materials is that they form heaps: Poured out from a vessel, they automatically form a layered structure with a peak somewhere close to the middle.
Necessary for this is shape: The dynamics of granular particles is governed by a competition of rolling and sliding. Spheres have not need to slide, they can roll with minimum resistance, and with pure rolling, heaps can and will disintegrate to single layers.
In our research, we model granular particles as polytopes (polygons in two dimensions, polyhedra in three dimensions) with friction, to obtain granular dynamics which is as realistic as possible: