particle stiffness scaling

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Hi,

I need this question to be answered, because I think if we write a paper, the reviewers will ask the same question: why scale with (r1+r2)/4?

Ning

Hi Ning,

My apologies. I didn't notice this question.

The various rotational bonded interactions (RotBonded, RotFriction, BrittleBeam etc.) by default scale the stiffnesses of individual particle-pair interactions according to linear elastic beam theory with the assumption that the beams are cylinders.

Beam theory provides analytical relationships for the various stiffnesses (normal, shear, bending, torsion) as a function of a Young's modulus E, Poisson's ratio and geometrical parameters (the cross-sectional area A and length, L of the beam). Specifically, for normal stiffness:

Kn = E . A / L

If we assume the beams are cylinders, we need to decide the radius (R) of the cylindrical beam. It is not obvious what is the best choice when two unequal-sized particles are to be connected. Various options exist:
1) arithmetic mean: R = (R1 + R2)/2
2) min. radius: R = min{R1,R2}
3) max. radius: R = max{R1,R2}
4) a constant
5) ...

When meanR_scaling=true (the default), the radius of the beams is equal to the arithmetic mean (option 1 above). Consequently, for normal stiffness scaling we have:

Kn = E . A / L = E. pi R^2 / (R1 + R2) = E . pi . ((R1+R2)/2)^2 / (R1 + R2) = E . pi . (R1 + R2) / 4

I hope this answers your question.

Cheers,

Dion

Hi Dion,

Thanks very much for the detailed reply. I'm happy with your explanation on the scaling law. Still one more question: since there is no `pi` in the code (effA = effR * effR), can I say the input parameter K is equivalent to E.pi in this case?

Ning

Hi NIng,

In fact the 'pi' is included but just not in the code fragment you are refering to. It is included as part of one of the constructors for the associated interaction group params classes. See for example line numbers 117-127 of Model/RotBondedInteraction.cpp. This is slightly convoluted but necessary to ensure the correct scaling for different choices of beam radius scaling (e.g. when meanR_scaling=false).

Consequently the 'normalK' input parameter is equal to the beam Young's modulus, E when scaling is used.

Cheers,

Dion

Hi Dion,

I did a small test on RotFrict model. From force and penetration calculation, I found the particle-particle stiffness is scaled by (r1+r2)/4 without a multiplier of pi. And the particle-wall stiffness is scaled by particle radius times pi (=wall_stiffness x radius x M_PI).

So RotBond model scales differently with RotFrict model. Have anyone also tested this?

Ning

Hi Ning,

Looks like you found an oversight/bug.

Try using FrictionPrms instead of RotFrictionPrms. This one should scale with pi factor.

The API docs for FrictionPrms are here:
http://esys.esscc.uq.edu.au/esys-particle_python_doc/snapshot/pythonapi/html/esys.lsm.LsmPy.FrictionPrms-class.html#__init__

Cheers,

Dion.

Hi Dion,

The FrictionPrms doesn't scale M_PI neither. I think there is an error in ./Python/esys/lsm/InteractionParamsPy.cpp:

In lines 619, 630, and 640,
CRotFrictionIGP(name, youngsModulus, poissonsRatio, dynamicMu, staticMu, 0.0, true, **,**) ## 9 parameters here.

There is an extra 'true' which makes the module cannot be properly mapped to CRotFrictionIGP in ./Model/RotFricInteraction.cpp which only requires 8 parameters when using Young's modulus and Poisson's ratio.

Ning

Hello everyone,

I'm wondering if anyone has confirmed this issue or I committed a mistake?

Ning

Hi,

I've committed the modification and it works well for both RotFrictionPrms and FrictionPrms. I'm wondering if I have access to contribute my corrections to the source code and how?

I didn't check the bonded model for the scaling issue. It would be better for someone with experience to double check it.

Ning

Hi Ning,

Could you please explain exactly what modification you made to get this working? If it is fairly simple, I will add it to the development version in the next few days.

Cheers,

Dion

Hi Dion,

Sure. It's fairly simple.
1. In ./Model/RotFricInteraction.cpp, delete line 46 and 49, and add to the following brackets {} (line 55):
{
    k = M_PI*kR;
    k_s = M_PI*kS;
}

2. And in ./Python/esys/lsm/InteractionParamsPy.cpp, remove the FIRST "true" in lines 619, 630, and 640.

Cheers,
Ning

Thanks Dion Weatherley, that solved my question.