ESyS-Particle

inconsistency between micro and macro quantities

Asked by ceguo

Hi everyone,

I am running a triaxial compression simulation (quasi-static deformation) using unbonded particles. The stress can be calculated using the formula "sigma = 1/V SUM(f * d)" suggested by Bathurst, 1985 from the microscopic quantities. Also we can calculate the principal stresses reading the wall forces from the field saver, i.e. from macroscopic quantities. It is expected that these two results should be consistant. But it seems from my simulation the former are usually smaller (may as much as 50%) than the latter. First I thought it may be attributed to non-quasistatic condition, but I set dt << 0.1*sqrt(m/k), e.g. (k = 3000, density = 2.7 and dt = 1.0e-5), also I used a large viscosity (0.7~1.0), but it doesn't work. May anyone can offer some advices.

By the way, I want to ask about the parameter scaling. I want to simulate the sand behavior, (Young's modulus 80 GPa, Poisson's ratio 0.25). According to Y. Wang et al, 2009, k = sqrt(2) E R / 2(1-2mu) = 113137 MPa (without multuplying R by set scale = True, so R will be multiplyed internally in esys). I use k = 1131 to adopt a smaller dt, so the confining pressure should be set to 0.002 to simulate 200 kPa in real. But I have to use a much larger value (about 2) to get satisfactory outputs. (The pressure is multiplyed by the area of the servo wall and applied in the servo wall.) Any experience sharing will be highly appreciated!

Tks,

Ning

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Dion Weatherley
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Dion Weatherley (d-weatherley) said : 		#1

Hi Ning,

Could you please provide the reference of the "Y. Wang et al, 2009" paper to which you refer in the original post?

To the best of my knowledge, the formulae derived by Dr. Wang in various papers all pertain to models comprised of particles with equal radius that are bonded together in a regular, crystalline arrangement (either a face-centred cubic or hexahedral close packing). In my experience, these formulae typically are not directly applicable to models with particles of variable size packed randomly in space. I would also expect these formulae to not apply to models comprised predominantly of unbonded, frictional particles.

You also mention using a smaller k (=1131) than the theoretical value of k=113137. Presumably this is to allow use of a larger timestep increment and hence lower the total number of timesteps. This is the "very soft contact" approximation" often used in DEM simulations to reduce the total computation time of simulations. I have found that, for fragmentation modelling at least, that using approximation is problematic. The issue is that this will change the effective units of measure (length, mass and time) used in the simulation relative to the real-world units. Invariably for studies in which models are calibrated against real-world experiments, one cannot use this "very soft contact" approximation.

I'm afraid I have no experience with triaxial compression of unbonded particles or the work of Bathurst (1985) so cannot comment on your first question. Hopefully someone else can offer some insight.

I hope this helps.

Cheers,

Dion.

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ceguo (hhh-guo) said : 		#2

Hi Dion,

Many thanks for your answers! The paper I referred to is (Y. Wang et al 2009) "A finite deformation method for discrete modeling: particle rotation and parameter calibration" published by Granular Matter. I think you are right the expression relating Young's modulus and particle stiffness only holds for monodispersed and bonded particles assemblies. Maybe I can try to use the Hertz-Mindlin contact model for my purpose.

I still want to ask about the quasi-static condition in esys. When I use the LinDamping and RotDamping I set the damping coefficient = 0.7 (as suggested in the tutorial ~0.5 for quasistatic), I found the kinetic energy (from the field saver e_kin) of the system is not very small (even larger) compared with the potential energy (from the field saver e_pot). Is there a upper limit for the value of the damping coefficient? Also I found when I change the value of the damping coefficient a lot, the macroscopic behavior of the simulation (e.g. strain-stress curve) may change considerably.

I am not sure the inconsistency between the macroscopic quantities (wall forces) and the microscopic quantities (contact forces) is due to non-quasistatic condition. But to make the simulation results more convincing, I should choose the parameters carefully. It is really a tough work.

Cheers,

Ning

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Best Dion Weatherley (d-weatherley) said : 		#3

Hi Ning,

Thanks for the reference. Just a small tip for the future: If a paper has only one or two authors, you should refer to the paper using (both) author(s) name(s) and not use 'et al.' This suffix is appropriate only if a paper has three or more authors. For the paper considered here, it would be Wang and Alonso-Marroquin (2009).

Regarding your questions about quasi-static conditions: If the kinetic energy is relatively large compared with the potential energy then you may not be simulating quasi-static conditions. However, the criterion for a simulation to be quasi-static is that the largest particle velocity should be a small fraction of either the loading speed or the compressional wavespeed (whichever is smaller). Just because the kinetic energy is large compared with the potential energy doesn't necessarily mean the simulation is not quasi-static.

Having said that, I've recently started to doubt whether the viscous damping implemented in LinDamping and RotDamping is appropriate for simulations of uni-axial or tri-axial compression. Viscous damping was originally designed to attenuate elastic waves in wave propagation simulations and it is known to not work well in simulations involving large deformations. Recently I implemented an alternative damping interaction, called local damping (Potyondy and Cundall, 2004) that might be worth a try instead of viscous damping.

The python syntax for implementing local damping is:

sim.createInteractionGroup (
  LocalDampingPrms(
     name="damping1",
     viscosity=0.7
  )
)

sim.createInteractionGroup (
  RotLocalDampingPrms(
     name="damping2",
     viscosity=0.7
  )
)

The viscosity (or damping coefficient) should be between 0 and 1. Higher values correspond to greater damping. A value of 0.7 is a good place to start. You will need to ensure you use a more recent development version of ESyS-Particle to use local damping. It was checked into the trunk in rev. 1257 around 27 Nov. 2009.

Local damping is rather extreme at removing kinetic energy from the system. You should carefully study the effect of adding local damping (and viscous damping) in any simulation. Both types of damping are "artificial" in the sense that they are used in DEM simulations to approximate a real physical situation (quasi-static conditions) whilst reducing the total number of timesteps to simulate that physical condition. Any "artificial" constraint like this should be used with caution. As you say: "...should choose the parameters carefully. It is really a tough work".

Good luck!

Dion.

Reference:
Potyondy, D. O., and P. A. Cundall. “A Bonded-Particle Model for Rock,” Int. J. Rock Mech. & Min. Sci., 41(8), 1329-1364 (2004).

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ceguo (hhh-guo) said : 		#4

Thanks Dion Weatherley, that solved my question.

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ceguo (hhh-guo) said : 		#5

Hi Dion,

Thanks for your help and useful tips. Regarding the reference question, if we want to write academic papers based on DEM simulations using ESyS-Particle, which literatures are we expected to cite?

Cheers,

Ning

Revision history for this message
Dion Weatherley (d-weatherley) said : 		#6

Hi Ning,

Unfortunately there are no recent papers describing the ESyS-Particle software itself. Steffen and I have started to write such a paper. In the meantime, the best reference for ESyS-Particle is the following:

Steffen Abe, David Place, and Peter Mora, A parallel implementation of the lattice
solid model for the simulation of rock mechanics and earthquake dynamics, Pure and
Applied Geophysics 161 (2004), 2265–2277.

If the journal in which you publish allows referencing of websites, perhaps you could also reference the launchpad website (https://launchpad.net/esys-particle)? If you do this, please also cite the paper above.

By the way, a (fairly) complele list of papers related to ESyS-Particle is available here:
https://twiki.esscc.uq.edu.au/pub/ESSCC/DemKurzAachen2009/ESyS-Particle_References.pdf

Might I also suggest that, when writing papers, you mention using the ESyS-Particle software in the acknowledgements including a link to the launchpad website (https://launchpad.net/esys-particle)?

Cheers,

Dion.