# Contact with friction example

hello, I have reproduced example 2 from this paper (https://www.researchgate.net/publication/226613820_BEM_and_FEM_analysis_of_Signorini_contact_problems_with_friction) and had to significantly change the recommended value for friction stick slope, by default CCX would have calculated K=130,000*50/100 = 650,000 but in order to get similar results to the paperI had to increase it to 6,500,000 (see graph displaying Ux vs x = D1 vs length, equivalent to Fig. 14 in the paper). Any thoughts? There have to be some better guidance regarding to what K, and lambda to choose, CCX default values look like a not very good option for most casesâ€¦

Hi @JuanP74 ,

You never ask so I assume this is going to be tough.

Some time ago I was doing contact slip testing and also found some discrepancy (much smaller). At the time I associated it to the deformation of the two surfaces in contact. The contact pressure between the two was modified and even some springs disconnected varying the expected value. Perhaps it is time to clarify this point in more detail.

Perhaps the recommended stick slope is suitable where sliding is much greater than deformation, like in some mechanism with moving stiff parts.

This case has deformation at the same order of magnitude as the sliding.

Well, itâ€™s an open question. I have relied too much in the past to bottled algorithms in commercial software and now I find I donâ€™t have solid criteria to select critical inputs.

Good point, indeed. So I need to find 2 cases where I can see both behaviours to compare.

Hi Juan,

I have set up the model from scratch using first my contacts standard criteria which a later explain.
The contact parameters have end up being mostly the same as in the paper.

I donâ€™t have nonlinear plain strain in MECWAY so I have assumed a tiny thickness (0.0001 mm).
The agreement is excellent.

The sticky value suggested by ccx works well for me as initial value (Kn/100). From my point of view the key problem is the normal Stiffness. (Kn unknown a priori)

E= 130.000 MPa
NP=50 MPa

Note Kn has force/volume units or Kn [MPa/mm] = [GPa/m]

Kn=130.000 * 50 = 6.500.000 [MPa/mm] = 6.500.000 [GPa/m] to start.

If Normal Pressure (NP) is difficult to pre-estimate, I simply use Kn=E [MPa] / mm .

HINT: Use contact clearance as in a convergence study. My reference value is how much penetration do I allow which I normally expect to be:

1E-5 mm - 1E-7 mm if the contact is the area of interest. (Interference fit or contact study like this one)
1E-3 mm - 1E-5 mm if Iâ€™m just looking for only compression support. Relaxing Kn (Clearance) speed up the convergence.

Comparing to the Paper.

Kn = 10^5 daN/mm2/mm = 1.000.000 [Mpa/mm] = 1.000.000 [Gpa/m] (Nice)
Kn= 10^6 daN/mm2/mm = 10.000.000 [MPa/mm]= 10.000.000 [GPa/m] (Results are said to be better. I would had use 6.500.000 [GPa/m] which is in between)

Results are in very good agreement.

Looks good but I had to change the lambda because of the Ux (D1) value as mentioned, since that value show where you have stick o slip. Check that variable, please, to see if also agrees.

I guess commercial software set a maximum allowable contact clearance and adjust Kn to fit.

This are the values for the Contact â€śCDISâ€ť.
Slightly different.
It capture the separation of the two extreme nodes . As they do not belong anymore to the contact node set , ccx doesnâ€™t provide CDIS for them.

Itâ€™s kind of strange that the paper include them. I think the base scale is wrong. Ccx aproach is more correct removing them.

Not sure what you mean, theyâ€™re plotting the D1 component of the nodes to check if there is slip, just comparing to the original position as the foundation is immovable. In my previous post you see where this displacement is zero, which is not the case in your plots. I had to increase lambda to fit this behaviour:

Notice the paper results with the authors analysis compared to Ansys:

Oh, sorry Juan. I thought you were validating or comparing similar formulations : ccx versus ANSYS.

So, you search for what K and lambda to choose in order to get similar results to the Boundary Layer Method. ÂżIs that correct?

ÂżIs it to clearly identify the boundary between Sticky / Sliding areas?

Yes, Iâ€™d like to know how to select the right K and lambda for ccx so I searched for analytical references, tests and other methods like BEM to compare.

Canâ€™t warranty 100% but Boundary method looks like a Heaviside function for the sticky slope. 0 tangential displacement up to the point where the shear stress exceeds the friction force. Then , detached, and free to slide. Would be like infinite tangential stiffness up to a certain shear. ÂżIsnâ€™t it?
That would make sense with the fact that increasing lambda you get a sharpy snap?

ÂżWouldnâ€™t that be like a brittle connection?. It doesnâ€™t seem necessarily better than the ccx actual approach.

Iâ€™m purely talking in terms of the physical response of such desired contact.

Just for your reference, attached the link to the file I was talking about at the beginning. My goal was to understand and be able to set up a friction brake which I could release when required. At that time, I was not concerned about some slip.
File is at the bottom of the post.

As far as I understand the FEM and BEM methods proposed in the paper are supposed to give the most accurate solution to the problem at hand without the need of choosing the appropriate penalty factors as it is the case with ansys and ccx. So the results in the paper can be used otherwise to understand how good penalty parameters should be chosen, for example in the way suggested by Victor.

Thanks. Iâ€™ll check it in detail.

I checked your model and it is intended to show when Coulomb friction isnâ€™t enough to hold the applied loads, Am I right? but my point is more related to this article:Frictional behavior

A finite value of the sticking stiffness may reflect a user-specified physical behavior or may be characteristic of the constraint enforcement method.

So it seems to me that there is more knowledge to be put in the selection of lambda than the ccx manual reflects. Looks like the suggested value only has the purpose of ensure convergence in the solution and not provided a guide to a particular behaviour of the model, which is left to the analyst.

So my suggestion would be that unless you have a specific understanding of the friction model, pure Coulomb needs a very steep slope but keeping in mind that may lead to convergence issues in some problems. Beware of pre-set values!!!

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Right. I was not worried about some slip.