Advice on brittle material simulation

Hi Juan,

- if you use a particle size range of 100-200 micron, i.e. r_max/r_min~2 you should get a packing with relatively high porosity. Not sure about the exact numbers. If you can't get to the 40% porosity directly you may try randomly removing particles from your packing until you get there. However, this would probably require switching from in-simulation model generation (via RandomBoxPack) to external geometry generation using the gengeo package and importing the geometry into you simulation via readGeometry().

- Youngs modulus and UCS can be adjusted independently using the parameters in BrittleBeamPrms. In my experience, the macroscopic Youngs modulus does scale fairly well (linearly) with the bond Youngs modulus (youngsModulus in BrittleBeamPrms) whereas UCS scales roughly with the cohesion parameter in BrittleBeamPrms. In your case (E~0.1-0.2GPa, UCS~1-2MPa) I'd suggest a ratio between youngsModulus and cohesion of ~100:1 as a starting point. Btw, are you working in dimensional or non-dimensional units in you simulations?

- for some more info on the relation between packing and stiffness / strength in DEM models have a look at Schöpfer et al., 2008, " The impact of porosity and crack density on the elasticity, strength and friction of cohesive granular materials: Insights from DEM modelling", Int. J. Rock Mech. Min. Sci.,

Steffen

Hi Steffen,
Thanks a lot for the help. I believe I'm working in dimensional units, just following the tutorial instructions for now, my r_max/r_min is ~0.2 since the tutorial said it's in mm. Am I mistaken?

Juan

Hi Juan,

Although you might be working in dimensional units, the ratio of of r_max/r_min is a non-dimensional quantity. As r_max >= r_min the quantity should also be >= 1. A ratio of 2 should give you a porosity between 35-40%.

Regards,
Will

I overlooked that you guys were talking about the ratio! I'm getting good results now. Thank you Steffen and Will

Hi all,

I'm trying to calibrate the simulation for a UCS between 1 and 2 MPa and failure at a strain of ~0.7%. So I am currently at the correct UCS range but at a breaking strain of 0.02%.
So far I have only been tweaking the parameters for bonded particle interactions but not the unbonded interactions -- do these play a significant role in the calibration as well?

  name="pp_bonds",
  youngsModulus = 500.0,
  poissonsRatio = 0.25,
  cohesion = 25,
  tanAngle = 30.0,
  tag=1

  name="friction",
  youngsModulus=5000.0,
  poissonsRatio=0.25,
  dynamicMu=0.4,
  staticMu=0.6

I've also noticed that the internal firction angle is very sensitive for these parameters and tweaking it a bit can outright ruin the simulation.
Again, thanks for all the help!

Hi Juan,

couple of questions w.r.t. the parameters you're using:
- why is the youngsModulus for your bonded interactions different from the one for the frictional interactions ? Particularly the fact that it is higher for frictional than for bondend interactions might lead to undesired effects.

- why are you using tanAngle=30 ? This would be a friction angle of ~88degrees (atan(30)) ? If you meant to use a 30 degree friction angle than tanAngle should be tan(30°)=0.577.

- the breaking strain should be at least on the same order of magnitude as the cohesion/youngsModulus ratio - which is 25/500 = 0.05 (i.e. 5%) in your case. So an observed breaking strain of 0.02% (i.e. 2e-4) suggests that something else is going wrong with your model. Have you checked your time step size and your deformation rate ?

Steffen

Hi Juan,

In answer to your question, "do the unbonded parameters play a role in macroscopic breakage?" -- yes, definitely, since the unbonded parameters play a role in the stress magnification which would lead to crack extension from bond breakage between a single pair of particles. You say you're getting the right UCS but a much lower breaking strain than is measured in your material. My guess is that the solution would be to have a much lower friction YoungsModulus since that would result in the two particles from a broken bond pair moving more easily relative to each other, thereby reducing stress concentration at the site of the broken bond (and thereby requiring a greater number of unrelated or scattered bond pairs to be broken to get material failure, hence increasing the breaking strain). My intuition could be wrong about the direction of the friction YoungsModulus, but at any rate, I'm sure you could match both UCS and breaking strain by playing around with the post-bond friction parameters. Good luck!