Definition of Yade's frictionAngle for a single material

Hi,
I'm modelling triaxial test and I play a lot with this parameter, in soil mechanics, angle of friction is about the behavior of the soil: The friction angle is a shear strength parameter of soils. Its definition is derived from the Mohr-Coulomb failure criterion and it is used to describe the friction shear resistance of soils together with the normal effective stress. In the stress plane of Shear stress-effective normal stress, the soil friction angle is the angle of inclination with respect to the horizontal axis of the Mohr-Coulomb shear resistance line (1). And I think that's what YADE is using.
I give you a demonstration of the definition of this term, I think it's clear for you.
http://i.imgur.com/QZ0Cr6m.png (2)

(1) - http://www.geotechdata.info/parameter/angle-of-friction
(2) - Soil Mechanic p.62 - Lambe

Thanks Nguyen.
if you look at [1] there is one thing I dont understand.
I give you an example:
in [1] you see a box which is placed on a plane. Mass of the box causes force N on the plane. Now I push the box with an increasing force T.
using the maximal possible T for which the box wont start sliding gives me a frictionAngle. (static friction)

If we assume that the box is already moving (with constant speed) there is an T for which acceleration will be zero - so velocity stays constant. This T gives an dynamic frictionAngle.

This leads to my second question from above: Does yade use static or dynamic frictionAngle

Concerning my first question - let us enhance this little example.
may the box be made of material1 and the plane of material2.
If you determine the frictionAngle it is valid for this pair of materials only.

Think of a different plane made of material3.
The experiment from above will give you a diffrent frictionAngle. But when you simulate this box on a plane in Yade both materials must be given a frictionAngle, from which the matchmaker [2] will use the lowest for calculation of interactions[3].

This leads to a problem: if frictionAngle of material1 is lower than material2 and material3 than the matchmaker will use its frictionAngle whatever plane it will be placed on. Hence force T would be equal for both planes. This does not go in hand with real experiments.

As I mentioned earlier - in my eyes frictionAngle cant be defined for a single material but for a pair of two materials.

---
[1] http://www.geotechdata.info/parameter/angle-of-friction
[2] https://yade-dem.org/doc/yade.wrapper.html#yade.wrapper.MatchMaker
[3] https://yade-dem.org/doc/yade.wrapper.html#yade.wrapper.Ip2_FrictMat_FrictMat_FrictPhys

Hello Eugen,

if you look at [1] there is one thing I dont understand.
> I give you an example:
> in [1] you see a box which is placed on a plane. Mass of the box causes
> force N on the plane. Now I push the box with an increasing force T.
> using the maximal possible T for which the box wont start sliding gives me
> a frictionAngle. (static friction)
>
> If we assume that the box is already moving (with constant speed) there
> is an T for which acceleration will be zero - so velocity stays
> constant. This T gives an dynamic frictionAngle.
>
> This leads to my second question from above: Does yade use static or
> dynamic frictionAngle
>

it is similar case as "young" or "poisson" parameters - each contact law
may consider this parameter in different way. The friction angle itself is
related to internal friction angle of a material [1] and (in case of
FrictPhys_CundallStrack) is used for Mohr-Coulumb plasticity condition

shearStress <= normalStress * tan(frictionAngle)

But in general (maybe not all contact laws) Yade uses static friction angle
between two individual particles.

It depends on the simulation setup and what you really call "friction
angle" (like young parameter, it is parameter of one bond, but real Young's
modulus of particle assembly is different). If you have a cube made from
spherical particles placed on "rough plane" made of spherical particles, it
would probably be possilbe (I am not sure) to get different values for
static and dynamic friction angle between such cube and plane (although
using only one parameter of contact law).

But you are rihgt, that these parameters could be documented better :-)

>
> Concerning my first question - let us enhance this little example.
> may the box be made of material1 and the plane of material2.
> If you determine the frictionAngle it is valid for this pair of materials
> only.
>
> Think of a different plane made of material3.
> The experiment from above will give you a diffrent frictionAngle. But when
> you simulate this box on a plane in Yade both materials must be given a
> frictionAngle, from which the matchmaker [2] will use the lowest for
> calculation of interactions[3].
>

Acoording to your link to MatchMaker, you can define what law will be used
for "averaging" (min, max, average..)

>
> This leads to a problem: if frictionAngle of material1 is lower than
> material2 and material3 than the matchmaker will use its frictionAngle
> whatever plane it will be placed on. Hence force T would be equal for
> both planes. This does not go in hand with real experiments.
>
>
see above.

> As I mentioned earlier - in my eyes frictionAngle cant be defined for a
> single material but for a pair of two materials.
>

it can be defined for two bodies (possible with the same material) and if
the material is composed of many bodies, it has some its own angle of
repose [1], which is related to (internal) friction ange of such material.

HTH
Jan

[1] http://en.wikipedia.org/wiki/Angle_of_repose

Hi Eugen,

All the current contact laws assume static=dynamic, because nobody really needed something else yet.
Writing a different laws with different friction in static vs. dynamic would not be difficult.

You are right, of course, friction gets meaningful only with a contact pair, but Yade's logic is to define the properties in materials first. Not really a problem when you are used to it.
When body1 and body2 have different values of friction, the minimum is used for the contact by default. More sophisticated combinations are possible with matchMakers (do you have something precise in mind?)

Bruno

hi Eugen,

I agree with Jan that the friction can be considered as static. Since the simulation (both static and dynamic) is computed each timestep, and system at each step = static.

@Hien Nguyen: not as what you said. The friction determined by Mohr-Coulomb theory is INTERNAL friction for macro behavior of material. It includes friction and interlocking, does not mean friction between 2 objects or 2 particles.

I don't see why computing at each step is static, nor why the contact laws would define only static friction.
The shear force at a sliding contact defines dynamic friction, right? In the current contact laws the maximum fs before sliding (static) and the fs during sliding (dynamic) are computed with the same angle. It simply means the assumption static friction = dynamic friction.
So FrictPhys::friction, is not "static OR dynamic", it is "static AND dynamic".

Eugen,

The three bodies problem you refer to is the classical caveat of computing contact parameters from bodies properties. I had the same problem years ago with PFC. But matchmakers gives you all freedom to solve this problem, as suggested by Jan.

Note that your three bodies problem has in fact an easy solution without matchMakers.
If you want friction f12 between b1 and plane 2, and friction f13 between b1 and plane 3, then why would you assign the minimum friction paramater to b1? You are not looking for troubles are you? ;)
Since b1's friction is a meaningless parameter with the only purpose of defining contacts friction, you will give it any value (say 6e66), then you will assign f12 to plane 2 and f13 to plane 3.

Of course, if we must have at the same time friction f23 between planes 2 and 3, we are toasted already, then goto: matchmakers.

Thanks again for all your help so far!
let me start with Jan:
@Jan
frictionAngle <-> internalFrictionAngle <-> contact law:
> it is similar case as "young" or "poisson" parameters - each contact law
> may consider this parameter in different way. The friction angle itself is
> related to internal friction angle of a material [1]
I'm using Law2_ScGeom_FrictPhys_CundallStrack and Law2_ScGeom_MindlinPhys_Mindlin right now. For a better impression what I'm using Yade for see this screenshot.
http://s7.directupload.net/images/130404/9x582i65.png
As you see there are several spheres inside a (green) facet cylinder. The grey facet cylinder is rotating around the z-axis on a circular path inside the green cylinder.
All the spheres in my application are bodies made of the same material (ceramic), I don't use clumps.
The cylinders are made of a different material. In some scenarios the cylinders are made of the same material (namely steel) - in other scenarios the grey cylinder is made of steel and the green cylinder is made of polyurethane [1] coated steel.
So I have three diffrent materials and need to specify material properties young, poisson and frictionAngle for each.

> ...and (in case of FrictPhys_CundallStrack) is used for Mohr-Coulumb plasticity condition
>
> shearStress <= normalStress * tan(frictionAngle)
So what happens if Mohr-Coulumb plasticity condition is hurt? Particles wont break, will they? Is it possible to apply a force on a single particle in a simulation? This way I could check what happens when Mohr-Coulumb plasticity condition is hurt.

> But in general (maybe not all contact laws) Yade uses static friction angle
> between two individual particles.
Do you mean static friction angle between two particles (e.g. spheres) made of the same material? (at least if I use these 2 mentioned contact laws) Because this would give a hint of how to determine the static friction angle exactly: follow method 2 or 3 from [2] with plane and box being made of identical material.

> It depends on the simulation setup and what you really call "friction
> angle" (like young parameter, it is parameter of one bond, but real Young's
> modulus of particle assembly is different). If you have a cube made from
> spherical particles placed on "rough plane" made of spherical particles, it
> would probably be possilbe (I am not sure) to get different values forexperiment
> static and dynamic friction angle between such cube and plane (although
> using only one parameter of contact law).
As mentioned above I dont use clumps, so I'm interested in assigning right material parameters to my (independent) spheres and my facet models. Following this frictionAngle of the material of the spheres means frictionAngle of a single sphere.

> Acoording to your link to MatchMaker, you can define what law will be used
> for "averaging" (min, max, average..)
Yes, I read about that. But I don't know of any appropriate mechanical theory that justifies choosing any of these laws. Considering the CundallStrack contactLaw (as you mentioned) this frictionAngle will be used for Mohr-coulomb plasticity condition only, right? So it is plausible to chose the minmal angle, because this material will fail first. But what about MindlinPhys_Mindlin?

>> As I mentioned earlier - in my eyes frictionAngle cant be defined for a
>> single material but for a pair of two materials.
>>
> it can be defined for two bodies (possible with the same material) and if
> the material is composed of many bodies, it has some its own angle of
> repose [1], which is related to (internal) friction ange of such material.
But how Yade uses frictionAngle is depending on contact law, right? According to Bruno - no contact law distinguishes between static and dynamic friction(angle). So again the question: is there any further use of frictionAngle than checking plasticity condition when using MindlinPhys_Mindlin?

@Bruno:
> When body1 and body2 have different values of friction, the minimum is used for the contact by default. More sophisticated
> combinations are possible with matchMakers (do you have something precise in mind?)
As I said before, I dont know the reason why the minimal value of friction is used. It would make sense if the value of friction (frictionAngle) is used for checking plasticity condition only in Yade.

@wasabi:
I agree that there is a difference between frictionAngle between two materials as shown in [2] and angle of internalFriction as mentioned in [3]. So if the frictionAngle was merely used for Mohr-Coulomb condition than it could be interpreted as angle of internal friction.

@Bruno:
> The three bodies problem you refer to is the classical caveat of computing contact parameters from bodies properties. I had
> the same problem years ago with PFC.
Could you please give a brief summary of your PFC problem and your solution? maybe this helps.

> Note that your three bodies problem has in fact an easy solution without matchMakers.
> If you want friction f12 between b1 and plane 2, and friction f13 between b1 and plane 3, then why would you assign the
> minimum friction paramater to b1? You are not looking for troubles are you? ;)
> Since b1's friction is a meaningless parameter with the only purpose of defining contacts friction, you will give it any value (say > 6e66), then you will assign f12 to plane 2 and f13 to plane 3.
Yes, this can be a great solution, providing that the dummy friction of b1 is used for that purpose only. I'm not sure about that

> Of course, if we must have at the same time friction f23 between planes 2 and 3, we are toasted already, then goto:
> matchmakers.
Good news are: I can guarantee that planes 2 and 3 arent longing for contact ;-)

What about this idea:
using method 2 or 3 from [2] with a box (material1) and a plane (material2) gives certain values for friction (angle). Is it possible to simulate a single sphere (material1) which is placed on a horizontal plane (material2). Now the sphere has to be forced to NOT roll but slide. If I apply a increasing horizontal force on the sphere it should at some point start sliding. Consequently I could check whether this happens at the expected magnitude of horizontal force.
A second way could be cluming two spheres together, both with material1, and again placed on a plane (material2). Now they there's no way than sliding if horizontal force is high enough. But I'm not sure if this will give the same result as the first setup...

---
[1] https://en.wikipedia.org/wiki/Polyurethane
[2] http://www.tribology-abc.com/abc/friction.htm
[3] http://en.wikipedia.org/wiki/Angle_of_repose
      it's interesting that the german version of this wikipedia page is relly diffrent vom the english one (any german speaking here?)
      http://de.wikipedia.org/wiki/Reibungswinkel

>As I said before, I dont know the reason why the minimal value of friction is used.

The hardness of the contact between talc and diamond is the hardness of talc. The logic is the same in our case for friction.
Would you suggest a better default behavior?
Since it is only a default it is not really important anyway. The good question is what physics you want to simulate, and this really depends on your materials, not on Yade. We can't decide for you.

>It would make sense if the value of friction (frictionAngle) is used for checking plasticity condition only in Yade.

I don't understand this statement.

>Could you please give a brief summary of your PFC problem and your solution?

2 groups of spheres (say A and B), 3 values of contact stiffness to be defined independently for A-A, A-B, and B-B.
Not possible if stiffness is assigned to materials A and B (3 equations, 2 unknowns...), which is the case in PFC and in YADE.
For PFC, there was simply no solution at that time. For Yade, there is now the matchmakers. They were introduced by Vaclav in response to a question very similar to yours. I don't know if they have been really used by somebody yet.

>Yes, this can be a great solution, providing that the dummy friction of b1 is used for that purpose only. I'm not sure about that

You can be sure. I wrote CundallStrack, and I know Hertz is using the same logic.

>What about this idea:

Are you speaking of experiments setup or simulation? If this is a simulation, this would be a sort of debugging, and I can tell you that you will find the expected result: fmax = weigth*tan(min(f1,f2)).

Hi, my 2cts.

You can have a look in the source code, where friction angle is
calculated and implemented [1], especially lines 67, 72, 231 and 383.
They will give you an exact information about friction angle in this
constitutive law in Yade. Actually, in other DEM-codes AFAIK the
implementation is almost the same.

I do not think, that the friction angle is the parameter, which will
sufficiently influence on the "macro"-results of your simulation. You
will, probably, get a noticeable difference, say, between mu=0 and
mu=0.2, but you will unlikely see a big difference between mu=0.2 and
mu=0.5. You should check and decide, whether you really need set the
friction angle so accurately.

Cheers,

[1] https://github.com/yade/trunk/blob/master/pkg/dem/HertzMindlin.cpp#L67

Hi Eugen,

Eugen Kubowsky is still having a problem:
> Thanks again for all your help so far!
> let me start with Jan:
> @Jan
> frictionAngle <-> internalFrictionAngle <-> contact law:
> > it is similar case as "young" or "poisson" parameters - each contact law
> > may consider this parameter in different way. The friction angle itself
> is
> > related to internal friction angle of a material [1]
> I'm using Law2_ScGeom_FrictPhys_CundallStrack and
> Law2_ScGeom_MindlinPhys_Mindlin right now. For a better impression what
> I'm using Yade for see this screenshot.
> http://s7.directupload.net/images/130404/9x582i65.png
> As you see there are several spheres inside a (green) facet cylinder. The
> grey facet cylinder is rotating around the z-axis on a circular path inside
> the green cylinder.
> All the spheres in my application are bodies made of the same material
> (ceramic), I don't use clumps.
> The cylinders are made of a different material. In some scenarios the
> cylinders are made of the same material (namely steel) - in other scenarios
> the grey cylinder is made of steel and the green cylinder is made of
> polyurethane [1] coated steel.
> So I have three diffrent materials and need to specify material properties
> young, poisson and frictionAngle for each.
>

In my opinion, the MatchMaker is perfect solution for such scenario (see
below).

>
> > ...and (in case of FrictPhys_CundallStrack) is used for Mohr-Coulumb
> plasticity condition
> >
> > shearStress <= normalStress * tan(frictionAngle)
> So what happens if Mohr-Coulumb plasticity condition is hurt? Particles
> wont break, will they? Is it possible to apply a force on a single particle
> in a simulation? This way I could check what happens when Mohr-Coulumb
> plasticity condition is hurt.
>

This law takes place in interactions, i.e. between two particles. If two
particles overlap, they generate some normal force
(Fn=normalStiffness*normalDisplacement). If they further slide or rotate,
this mutual transverse displacement causes shear force
(Fs=shearStiffness*shearDisplacement). In continuum plasticity, this would
be trial stress. Now the plasticity condition is checked Fs.norm() <=
normalForce*tan(frictionAngle). If it is satisfied, nothing happens. If it
is not, then the force (while preserving its direction) is reduced such
that its magnitude satisfied condition Fs.norm() =
normalForce*tan(frictionAngle). In continuum plasticity, this would be
stress return.

>
> > But in general (maybe not all contact laws) Yade uses static friction
> angle
> > between two individual particles.
> Do you mean static friction angle between two particles (e.g. spheres)
> made of the same material? (at least if I use these 2 mentioned contact
> laws) Because this would give a hint of how to determine the static
> friction angle exactly: follow method 2 or 3 from [2] with plane and box
> being made of identical material.
>

Yes (also according to Bruno's answer), these contact laws does
not differentiate between static and dynamic, simply uses plastic condition
mentioned above.

>
> > It depends on the simulation setup and what you really call "friction
> > angle" (like young parameter, it is parameter of one bond, but real
> Young's
> > modulus of particle assembly is different). If you have a cube made from
> > spherical particles placed on "rough plane" made of spherical particles,
> it
> > would probably be possilbe (I am not sure) to get different values
> forexperiment
> > static and dynamic friction angle between such cube and plane (although
> > using only one parameter of contact law).
> As mentioned above I dont use clumps, so I'm interested in assigning right
> material parameters to my (independent) spheres and my facet models.
> Following this frictionAngle of the material of the spheres means
> frictionAngle of a single sphere.
>

This my note probably does not fit to your scenario, sorry, just ignore it
:-)

>
> > Acoording to your link to MatchMaker, you can define what law will be
> used
> > for "averaging" (min, max, average..)
> Yes, I read about that. But I don't know of any appropriate mechanical
> theory that justifies choosing any of these laws. Considering the
> CundallStrack contactLaw (as you mentioned) this frictionAngle will be used
> for Mohr-coulomb plasticity condition only, right? So it is plausible to
> chose the minmal angle, because this material will fail first. But what
> about MindlinPhys_Mindlin?
>

Just an example (I have no idea what the parameters should be in reality):
for the materials of particles, you know frictionAngle = 45 deg,
particles-steel = 20 deg and particles-coated steel=10 deg. So you simply
define frictionAngle:
particles: 45 deg
steel: 20 deg
coated steel: 10 deg
and use MatchMaker to use minimal value. If the values are oposite, use
maximum, Therefore interpaticle interactions will use their own friction
angle and interactions between particles and other material will inherit
parameters from the other materials.

>
> >> As I mentioned earlier - in my eyes frictionAngle cant be defined for a
> >> single material but for a pair of two materials.
> >>
> > it can be defined for two bodies (possible with the same material) and if
> > the material is composed of many bodies, it has some its own angle of
> > repose [1], which is related to (internal) friction ange of such
> material.
> But how Yade uses frictionAngle is depending on contact law, right?
> According to Bruno - no contact law distinguishes between static and
> dynamic friction(angle). So again the question: is there any further use of
> frictionAngle than checking plasticity condition when using
> MindlinPhys_Mindlin?
>

According to quick look to source code, it has no other effect.

>
> @Bruno:
> > When body1 and body2 have different values of friction, the minimum is
> used for the contact by default. More sophisticated
> > combinations are possible with matchMakers (do you have something
> precise in mind?)
> As I said before, I dont know the reason why the minimal value of friction
> is used. It would make sense if the value of friction (frictionAngle) is
> used for checking plasticity condition only in Yade.
>

I will just repeat Bruno's answer. Some procedure how to deal with two
different material properties should be set as default. In this case, the
minimum is chosen, nothing else :-) for more sophisticated dealing, use
MatchMaker.

>
> What about this idea:
> using method 2 or 3 from [2] with a box (material1) and a plane
> (material2) gives certain values for friction (angle). Is it possible to
> simulate a single sphere (material1) which is placed on a horizontal plane
> (material2). Now the sphere has to be forced to NOT roll but slide. If I
> apply a increasing horizontal force on the sphere it should at some point
> start sliding. Consequently I could check whether this happens at the
> expected magnitude of horizontal force.
> A second way could be cluming two spheres together, both with material1,
> and again placed on a plane (material2). Now they there's no way than
> sliding if horizontal force is high enough. But I'm not sure if this will
> give the same result as the first setup...
>

Yes, you can play with such simple examples if you really want to
understand what is hapenning :-) in your second example, the force wuold
probably be double as there are two particles :-)

cheers
Jan

I'd like to reopen this thread.
I'm trying to implement a matchmaker for the friction angle.
How can I do so?
Is the match maker kind of a further "engine" in the simulation?

Thanks,
Alex

Hi Alex

the friction angle is defined with the material and usually set in the Ip2
functors where the minimum of the material of the two particles in contact is
used. However, some Ip2 functors (e.g. Ip2_FrictMat_FrictMat_FrictPhys [1])
support MatchMakers as well, try something like this:

...
Ip2_FrictMat_FrictMat_FrictPhys(frictAngle=MatchMaker(matches=((steelId,shotsId,phi1),
(shotsId,shotsId,phi2))))
...

Please note the different in name: frictAngle instead of frictionAngle.

HTH Klaus

[1] https://yade-dem.org/doc/yade.wrapper.html?highlight=frictangle#yade.wrapper.Ip2_FrictMat_FrictMat_FrictPhys.frictAngle

On Wednesday 04 September 2013 13:51:11 Alexander Eulitz [Eugen] wrote:
> Question #225776 on Yade changed:
> https://answers.launchpad.net/yade/+question/225776
>
> Status: Answered => Open
>
> Alexander Eulitz [Eugen] is still having a problem:
> I'd like to reopen this thread.
> I'm trying to implement a matchmaker for the friction angle.
> How can I do so?
> Is the match maker kind of a further "engine" in the simulation?
>
> Thanks,
> Alex
>
> --
> You received this question notification because you are a member of
> yade-users, which is an answer contact for Yade.
>
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Thank you Klaus, for your advice. Right now I'm using a diffrent IP2 functor: Ip2_FrictMat_FrictMat_MindlinPhys() according to [1] it does not have a frictAngle Attribute.
My Law2 is Law2_ScGeom_MindlinPhys_Mindlin()

How can I nake use of a match maker for friction angle in this case?

thanks, Alex

Hi Alex

it's implemented now [1]. Just update your source files an re-compile the code
and you will be able to use it.

Klaus

[1]
https://github.com/yade/trunk/commit/bd698e9a7aa9e05dfc7ead6293e3dd35a8f960d9

On Friday 06 September 2013 10:11:40 Alexander Eulitz [Eugen] wrote:
> Question #225776 on Yade changed:
> https://answers.launchpad.net/yade/+question/225776
>
> Status: Answered => Open
>
> Alexander Eulitz [Eugen] is still having a problem:
> Thank you Klaus, for your advice. Right now I'm using a diffrent IP2
> functor: Ip2_FrictMat_FrictMat_MindlinPhys() according to [1] it does not
> have a frictAngle Attribute. My Law2 is Law2_ScGeom_MindlinPhys_Mindlin()
>
> How can I nake use of a match maker for friction angle in this case?
>
> thanks, Alex
>
> --
> You received this question notification because you are a member of
> yade-users, which is an answer contact for Yade.
>
> _______________________________________________
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> Post to : <email address hidden>
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--
Dr. Klaus Thoeni - Centre for Geotechnical and Materials Modelling
Civil, Surveying and Environmental Engineering - Engineering Building EA
The University of Newcastle, Callaghan, NSW 2308, Australia
web: http://www.newcastle.edu.au/research-centre/cgmm
phone: +61 (0)2 4921 5735

Thanks a lot Klaus.
But isn't this change already part of daily build?

Daily-builds are currently broken because of failing PFV-test.

Anton

2013/9/8 Alexander Eulitz [Eugen] <email address hidden>:
> Question #225776 on Yade changed:
> https://answers.launchpad.net/yade/+question/225776
>
> Status: Answered => Solved
>
> Alexander Eulitz [Eugen] confirmed that the question is solved:
> Thanks a lot Klaus.
> But isn't this change already part of daily build?
>
> --
> You received this question notification because you are a member of
> yade-users, which is an answer contact for Yade.
>
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