Parameter values for Hertzian Viscoelastic interaction with friction

Hi Dennis,

There are no tables (that I know of) listing model parameters for particular materials. Typically, for any given model arrangement (and target application), it is necessary to undertake an application-specific calibration exercise. This calibration exercise is different for different modelling scenarios and the choice of particle-pair interaction types.

For example, if one wishes to model rock breakage then calibration is done using uniaxial compression simulations to obtain desired macroscopic mechanical properties (such as Young's modulus or peak compressive strength) by tuning model parameters. For granular media flow studies, a better method is to use shear-cell or tri-axial compression simulations to tune the macroscopic (or bulk) friction coefficient of the material.

As I do not regularly use the Hertzian interactions in my own ESyS-Particle simulations, I cannot really help with "typical values". Perhaps another user with more experience can assist?

Cheers,

Dion

Hi Dion,

  Thanks for your reply. I just want to simulate a simple flow of dry sand on some narrow channel. So, I want to use Hertzian contact interaction plus friction. I suppose Hertzian contact is more approriate than Hookean contact interaction.
Are these values reasonable? dynamic mu = 0.6, Poisson ratio= 0.2-0.4, Young's modulus: 10^5 N/m.

Sincerely,

Dennis

Hi Dennis,

Those values would certainly be a reasonable starting range. Here are a couple of issues you may need to bear in mind though:

1) the bulk friction coefficient of a bed of particles is only weakly dependent upon the friction coefficient (dynamic and/or static mu). Particularly if you represent your sand grains as individual spheres, the bulk friction will be quite low (around 0.2-0.3 from memory) regardless of your choice of friction coefficient. A number of researchers have shown that realistic bulk friction coefficients can only be achieved by modelling sand grains as clusters of bonded particles. Typically the clusters only need a few particles (between 2 and 10) in order to achieve realistic bulk frictional properties. The key point is that geometrical interlocking between the clusters greatly increases rolling resistance and hence the bulk frictional response. One of my colleagues has successfully used hexagonal aggregates to represent sand grains in 2D flow simulations.

2) for materials handling or granular flow simulations, the requirement to model large displacements typically results in very long run-times for simulations. It is fairly usual practice in these situations to use a "soft contact" approximation i.e. artificially reduce the Young's modulus in order to increase the maximum stable timestep increment. It is common to reduce the Young's modulus by up to 1000x (i.e. 10^2 instead of 10^5). I personally prefer to stick with relatively high stiffnesses though (10^3 or 10^4). It is also important to do a few simulations with different stiffnesses to ensure the soft contact approximation is not significantly altering the dynamics you are interested in measuring/studying.

I hope this helps. As always, have fun!

Cheers,

Dion

Hi Dion,

   Thanks Dion. It really helps a lot! I'll just have to construct a box containing unbonded clusters of sand grains and allow it
to collapse over the channel. I hope this is not too much to ask but is there some examples in constructing box
with clusters of grains? I seen an example in gengeo but is in only in 2D.

dennis

Hi Dennis,

> the bulk friction coefficient of a bed of particles is only weakly dependent upon the friction coefficient
> (dynamic and/or static mu). Particularly if you represent your sand grains as individual spheres, the bulk
> friction will be quite low (around 0.2-0.3 from memory) regardless of your choice of friction coefficient.
For details, see Abe & Mair, 2009, "Effects of gouge fragment shape on fault friction: New 3D modelling results", Geophys. Res. Lett.

> I seen an example in gengeo but is in only in 2D
have a look at the gouge_example.py in the gengeo examples - that one is 3D.

Steffen

Hi Steffen,

  Thanks for pointing me to that example! I clearly failed to notice that one.
I just have some few questions on the code fragment below from gouge_example.py:

...
mntable = CircMNTable3D (
   minPoint = minPoint,
   maxPoint = maxPoint,
   gridSize = 2.5,
   numGroups = 3
)

packer = InsertGenerator3D (
   minRadius = minRadius,
   maxRadius = 0.4,
   insertFails = numInsertFails,
   maxIterations = 1000,
   tolerance = 1.0e-6
)
.........

 What does numGroups mean? Is this the initial number of grains? Im a little bit confused about this.
As suggested by Dion, about 2-10 particles should compose a cluster to have a realistic bulk
friction so if I represent sand grains with a radius of r=1.0mm (V=(4/3)*pi*r^3) then in the packer i should
have minRadius about 0.5 and maxRadius about 0.7 to have a cluster with 3-8 particles in it. Is this correct?
Lastly, how do I set the density of particles? Can I set this in the esys code or in gengeo directly?
Im going to construct a 10 cm^3 of unbonded sand particles with this example.

Sincerely,

dennis

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Hi Dennis,

> What does numGroups mean?

The MNTables in gengeo can handle multiple 'Groups' of particles. This can be useful for bonding and tagging different subgroups of particles differently. One should be careful though to ensure that particles within different groups reside in non-overlapping volumes. If the volumes overlap, the two groups of particles will overlap each other as the packer does not check whether particles from other groups reside within a given volume during generatePacking.

In the case of the gouge example, the three groups correspond to (1) the gouge grains within the shear cell, (2) the top driving plate and (3) the bottom driving plate.

> the packer i should have minRadius about 0.5 and maxRadius about 0.7 to have a cluster with 3-8 particles in it. Is this correct?

Sounds about right to me. Of course one normally will need to experiment a bit with these sort of parameter values.

> Lastly, how do I set the density of particles?

Particle densities are set in the ESyS-Particle script using sim.setParticleDensity(tag,density) where 'tag' is the tag of the particles whose density will be set and 'density' is the desired density. Best to do this straight after sim.readGeometry(..).

Cheers,

Dion

Hi Dennis

The Hertzian viscoelastic and friction interaction was implemented by my group as a contribution to ESyS-particle.

The description of the interaction and the test we have done to choose the proper values of the parameters are described in:
“Granular physics in low-gravity environments using DEM” (2012) G. Tancredi, A. Maciel, L. Heredia, P. Richeri, S. Nesmachnow, Monthly Notices of the Royal Astronomical Society, 420, 3368-3380.

If you do not have access to this article, please, let me know and I send you a copy.

Best regards

Gonzalo