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# a "contact sport" between academics

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Recently, there was a big competition announced for rough elastic adhesive contact --- by Martin Muser as organizer. This was published in Tribology Letter, involved the effort of many groups in the world, and finally got even a commentary in Science by Rob Carpick.

The **contact sport **of rough surfaces RW **Carpick** - Science, 2018 - science.sciencemag.org

I here make some critical questions and critical comments, some of which of course go beyond the original scope of the Contact Challenge.

Tribology Letters (2018) 66:37 https://doi.org/10.1007/s11249-018-0985-2

COMMENT A Comment on “Meeting the Contact‑Mechanics Challenge” by Muser et al. [1]

Michele Ciavarella1 Received: 31 August 2017 / Accepted: 15 January 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018

Anyway, we also argue that Persson's theory are based on many "corrective factors and functions" (while the other theories haven't been developed so in details).

- Muser's reply is an interesting paper on its own, but NOT a reply to my comment. Maybe this is because my comment was too wide and not just a comment to the "contact challenge"
- Muser does not answer about the corrective factors, despite he himself dedicates an entire paper to finding new ones for elastic thin slabs, for which they are completely different from the halfplane case. But it is in his rigth to do so.
- Muser does not answer about the exact equations Persson was using. Maybe Persson should be asked for this.
- Muser does not answer about the findings of Carbone, which in 1D seems NOT to require fudge factors. But this is of course not so much to do with the Contact Challenge paper so perhaps I should have asked Carbone instead.
- Muser does not answer about the fact that in tribology, we have not made much progress with Persson's theory, NOBODY can predict friction coefficient, wear coefficient, etc. using the fantastic fractal rough gaussian surfaces. Besides, in experimental measurements of real surfaces, they are NON gaussian! So Persson's theory does NOT apply! Even his own company shows experimental measurements which are very far from Gaussian http://multiscaleconsulting.com/index.php/software/power-spectrum. But again, Muser's choice is legitimate not to answer this.
- Muser does not answer about the fact that Weierstrass function model I introduced in 2001, my most cited paper he says, may be NOT realistic, but in fact shows ALL the conclusions that Persson obtained the same year, with gaussian rough random surfaces.
- Muser is fascinated by the physics and mathematics of fractals, and this is ok, but what about REAL tribological problems?
- Muser does not answer about the large adhesion case, where Persson's theories do not equally work. But this of course would require a new "Contact Challenge"
- Muser does not answer about why he did NOT clarify that people could partecipate also with PARTIAL ANSWERS to the Contact Challenge like with a VERY simple GW theory. But this is not important.
- Muser does not answer about the real FUTURE problems of tribology.
- Muser closes his reply with a very negative and bitter note, but I think the exchange of comments was useful, as only debates can improve our understanding. I am thankful to Nick Spencer director of ETH lab of tribology and Editor of Tribology Letters, on how he handled this difficult conflictual debate.
- Muser does not explain why we did setup a challenge with a surface, after these fitting functions worked reasonably well. Why this case should be so important?

A reply also to Carpick very "US-american" -style of Contact Challenge in Science :- Since the times of Leonardo da Vinci, we haven't made much progress, as friction coefficient **(which Leonardo suggested would be 0.25, not a bad estimate at all!)** has to be measured, and Persson's theories do *not help* in this. Nor on wear or lubrication problems, as one needs to measure a number of similar experimental coefficients.

On the contrary, I am quite convinced that if with fractals we have not made progress in 50 years, this is because the main ingredients are elsewhere.

And Leonardo in 1500 was generally quite correct --- friction coefficient is close to 0.25.

Interestingly, **we completed a big review paper of tribology lately, and Martin Muser and I are coauthor!! **

I must THANK Nick Spencer very much for how he dealt with the amusing debate between me and Martin Muser.

Martin Muser paper contains interesting new considerations, never appeared before, and even my contribution is, I hope, interesting.

What we need to decide is: what is the avenue for future directions?

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## Comments

## Contact mechanics challenge results: a follow up discussion

Featured in this nice tribology web site

## in general, very interesting web site on tribology

http://www.tribonet.org/

## The adhesion paradox in wear law

A very debated topic nowadays is wear, which still remains one of the major unsolved problems in tribology. We are almost stuck at the Reye's hypothesis (1860) as also the more recent Archard's law seems to be in contradiction with recent experiments. Recently some attention has been paid to the Rabinowicz criterion, which is based on the competition between plasticity and adhesion. Unfortunately, the most of the papers on "adhesive wear" do not consider adhesion for determining the actual contact size!

We have addressed this problem here: https://www.researchgate.net/publication/323028278_THE_SPORT_OF_ROUGH_CO...

Abstract:In a recent paper inScience, namely, “The Contact Sport of Rough Surfaces”, Carpick summarizes recent efforts in a “contact challenge” to predict in detail an elastic contact between the mathematically defined fractal rough surfaces under (very little) adhesion. He also suggests the next steps that are needed to “fulfill da Vinci’s dream of understanding what causes friction”. However, this is disappointing as friction has been studied since the times of Leonardo and in 500 years, no predictive model has emerged, nor any significant improvement from rough contact models. Similarly, a very large effort we have spent on the “sport” of studying rough surfaces has not made us any closer to being able to predict the coefficient of proportionality between wear loss and friction dissipation which was already observed by Reye in 1860. Recent nice simulations by Aghababaei, Warner and Molinari have confirmed the criterion for the formation of debris of a single particle, proposed in 1958 by Rabinowicz, as well as Reye’s assumption for the proportionality with frictional loss, which is very close to Archard anyway. More recent investigations under variable loads suggest that Reye’s assumption is probably much more general than Archard’s law. The attempts to obtain exact coefficients with rough surfaces models are very far from predictive, essentially because for fractals most authors fail to recognize that resolution-dependence of the contact area makes the models very ill-defined. We also suggest that in the models of wear, rough contacts should be considered “plastic” and “adhesive” and introduce a new length scale in the problem.## The references for the excellent works of Molinari at EFPL

Antonio

you should mention that we strongly refer to recent excellent work of the group of J. F. Molinari at EPFL in top journals.

Critical length scale controls adhesive wear mechanismsR Aghababaei, DH Warner, JF

Molinari- Nature communications, 2016 - nature.com [CITATION] Achard got it right: insights from a cohesive model (invited workshop)JFMolinari, R Aghababaei… - CECAM Workshop, he …, 2016 - infoscience.epfl.ch On the debris-level origins of adhesive wear…, DH Warner, JFMolinari- Proceedings of the …, 2017 - National Acad Sciences Mechanics of surfaces: a new look at the old problem of wear…, DH Warner, JFMolinari- Tribology & Lubrication …, 2017 - search.proquest.com and some more recent papers which JF Molinari kindly gave us in advance, as they are still under review.## A new book in Contact Mechanics

The topic of Contact Mechanics and also rough surfaces is covered in this book by J R Barber about to appear.

## The debate between me and Bo Persson continues on Researchgate

See at this link

https://www.researchgate.net/publication/322867618_A_Comment_on_Meeting_...

6d ago Giuseppe Carboneadded a commentThe reply is also interesting: http://www.lmp.uni-saarland.de/wp-content/uploads/2018/02/response.pdfRecommendedReply

5d ago Michele Ciavarellaadded a commentsee also why Muser did not really reply here http://imechanica.org/node/22108 with 12 questions re explained to Muser who avoided them.....Reply 3d ago Alessandro Cabboiadded a commentHi Michele, I read your comment on Muser's paper and Muser's reply as well. The debate is interesting, and I was wondering if it is still going on. Unfortunately, I cannot give a constructive feedback on both letters since I am keeping myself at a "safe" distance from the topic concerning "fractal…RecommendedReply

## Cabboi, Carbone, Persson

Michele Ciavarella

dear Bo I agree your theory is an improvement over GW in some respects, which appear important only when we deal with indeed "fractals", or broad multiscale surfaces. But this doesn't improve our understanding of friction. My main points are (i) that Muser did not answer any of my question, which you can find listed as "12 questions" in http://imechanica.org/node/22108 ----- please answer. And that your theory does not change anything in terms of actual "prediction" of friction coefficient. Please provide examples where your theory, especially since you have a commercial operation (and this can be considered by many as "pollution" in science and conflict of interest), and therefore you should be able to explain where you solved any real problem with including roughness ----------- this has NOT to include arbitrary cutoff in the fractal description, such as the ridicoulos choice of truncating the spectrum to h' rms=1.3 which you do with viscoelastic friction. RegardsMike

Bo Persson

Hi, I do not like fractals very much either and my theory has really nothing to do with fractals, it only require roughness on many length scales which is true for all surfaces in nature and engineering. In my theory I read in the surface roughness power spectra numerically and I do not care if it is a power low in the wavenumber or not! Still many surfaces is a power low in the wavenumber and can be usefully classified with the exponent! The GW theory does NOT predict the linearity between contact area and normal force and my theory was the first one to do so and even the first version of this theory gives the contact area to within ~ 20% of the exact numerical result. Taking into account all the complications in real life situations (e.g. elastic non-linearity) there is no point in trying to do better! As I have stated before, most articles and comment of Ciavarella are scientific pollution and what he wrote above is a typical example of this.I have only one interest in science: the truth!

Michele Ciavarella

Alessandro,you are quite rigth to keep at far distance from this useless academic area. My good friend and father of fracture mechanics, Jim Rice of Harvard University, told me that he was sharing the corridor with Benoit Mandelbrot and made friend with him. Only years later did he found that Benoit had published a well known paper in Nature where he claimed that fracture surfaes are fractals!Jim Rice has never used fractals, yet he has dominated the field of fracture mechanics. If fracture surfaces were fractals, or if this were important, Jim Rice would have noticed.Similarly, if the fractality of surfaces were anything like important in tribology, all these speculations about Persson's theory being better than GW, would have produced some progress. And they have.Another big, Ken Johnson, never really got involved into the GW problem, because he mentioned the qualitative results about linearity of contact area and load, in his book, and that was enough for him!Thanks for your interest. You are a promising and clever scientist, don't get the smoke in your eyes, think with your own brain.Mike

## my reply to Dr. Bo Persson

and Bo, when I say "fractals" are not important, I do NOT mean only the power law PSD, but all multiscale effects are not important, as far as I can see.

It is a pollution in the literature to invade with many articles raising hopes that these multiscale effects have anything predictive at all...But this is just my humble opinion, you certainly now agree on power-law PSD are not relevant, but I do not see why the NON-power law PSD are relevant also!

I understand of course you have valid reasons to promote your nice solutions, also commercially, with http://multiscaleconsulting.com/ which, paradoxically, contains information and diagrams that surfaces are NOT gaussian, so your theory cannot be used anyway.....

Regards

Mike

## in the commercial site of Persson surfaces are non Gaussian!!!

http://multiscaleconsulting.com/index.php/software/power-spectrum

The influence of roughness on the adhesion and frictional properties is mainly determined by the surface roughness power spectrum C(q) (or power spectral density) which is the most important quantity characterizing roughness. The surface roughness power spectrum fully characterizes all statistical properties of a measured surface. This means that all available information on the roughness is uniquely preserved in this quantity. It can be calculated directly from nearly any measured topography using our power spectrum software. This means that the power spectrum software is the perfect tool to further analyze your topography files and to calculate the input files necessary for our contact mechanics and rubber friction software. Note that while the root mean square roughness is usually dominated by the longest wavelength surface roughness components, higher order moments of the power spectrum such as the average slope or the average surface curvature are dominated by the shorter wavelength components. All these roughness parameters have therefore one thing in common, they do not describe the surface properties on different length scales. However it has been found that this is necessary to understand the true contact area between a tire with the road surface. It is hence not enough to gather information about a measured topography by only calculating the standard roughness parameters which exist for a long time already. The surface roughness power spectrum is the only statistical quantity which covers roughness properties over all length scales without loosing information over the surface measured. This is actually very important because practically all macroscopic bodies have surfaces with roughness on many different length scales. When two bodies with nominally flat surfaces are brought into contact, real (atomic) contact will only occur in small randomly distributed areas, and the area of real contact is usually an extremely small fraction of the nominal contact area. The contact regions can be visualized as small areas where asperities from one solid are squeezed against asperities of the other solid; depending on the conditions the asperities may deform elastically or plastically. How large is the area of real contact between a solid block and a substrate? This fundamental question has extremely important practical implications. For example, it determines the contact resistivity and the heat transfer between the solids. It is also of direct importance for wear and sliding friction, e.g., the rubber friction between a tyre and a road surface, and has a major influence on the adhesive force between two solid blocks in direct contact. The power spectrum calculator offers a quick, intuitive and hence easy to use software for calculating the surface roughness power spectrum of all kinds of different input formats.The figure below shows the latest Windows version of the program. After specifying the format type and some other important information about the topography file, like how many points in x and y-direction or the lattice constant between two points, one can choose between calculating the full, top or bottom power spectrum. Windows Version of the power spectrum software

When the calculation is finished successfully it is possible to directly check the power spectrum as shown below. The power spectrum software will give you in addition to the power spectrum many other important parameters. This includes different roughness parameters as for example the rms roughness value or the rms slope.

The surface roughness power spectrum

Here we show two other quantities which can be very to check after the power spectrum has been calculated as they contain very useful information. On the left is the height probability distribution while on the right we show the slope probability distribution. It is recommended to check these two curves after the calculation is finished to make sure that the results are reasonable and consistent with the power spectrum.

## I apologize for one of the questions to Muser -- 9

I must apologize for one point 9 in my questions to Muser. It is not true that he did not permit me to partecipate. I apologize and corrected.

## some more clarifications

I would specify that my statements are general and do not mean to say that Muser was in any way dishonest or falsifying any of the process of the "contact mechanics" challenge.

But the situation is simply that I raise points, also in my "comment" to the "contact challenge", which are difficult questions and do not necessarily pertain to the contact-mechanics challenge.

In a sense, it may look misleading and too much an attack to Muser that I raise these questions.

Muser is a very strong scientist, with very strong honest behaviour, and I have no intention to claim otherwise.

These questions are purely scientific debates. Unfortunately the way the "contact challenge" is organized, being Persson's theory, for that specific case, very well organized, makes all other theories less strong.

Muser was not in a good position to answer all my questions. His reply is a very interesting scientific paper.

The fact that we collaborated on a review paper shows that we are very good collegues and friends!

Future directions in tribology require more discussion.

You should make clear these things clear in an extra blog. I am seriously concerned about the damage your blog did and I want damage control to the largest possible degree. You are the only person who can fix this right now.

## the big review paper with my good friend Muser has appeared!

Modeling and simulation in tribology across scales: An overviewTribology International

Available online 12 February 2018

In Press, Accepted Manuscript — Note to users

Modeling and simulation in tribology across scales: An overview ☆

Show less

## by the way, I forgot to check if my BAM model works fine

By the way, this imechanica discussion makes me wonder why I did not check if my BAM model

http://imechanica.org/node/22131

works fine with the "Contact Challenge" surface. One reason may be that I developed BAM after the contact challenge results were collected.

It should be easy to do it, except to find the time!

Anyone willing to do it?

## BAM model and "Contact Challenge" surface

Dear Prof. Ciavarella,

I truly do not wish to be "cheeky" or disrespectful, but I find it remarkable that any researcher could refrain from the tantalising task of checking their own model against published data: is it not one of the most exciting aspect of modelling?

I hope you will find the time to check your BAM model with the "Contact Challenge" surface: regardless of the results it would certainly add value to this interesting discussion.

Best Regards

## BAM model and "Contact Challenge" surface

Dear Prof. Ciavarella,

I truly do not wish to be "cheeky" or disrespectful, but I find it remarkable that any researcher could refrain from the tantalising task of checking their own model against published data: is it not one of the most exciting aspect of modelling?

I hope you will find the time to check your BAM model with the "Contact Challenge" surface: regardless of the results it would certainly add value to this interesting discussion.

Best Regards

## of course, it is in our to-do-list, but the idea came recently!

You are not disrespectful at all. I agree with you.

The BAM model was validated, in the original paper, with pull-off data, which are much MORE difficult to predict with any other theory ---- including all Persson's theory.

The case of the Contact Challenge is relatively TRIVIAL, and with BAM model, given it is a very first approximation single closed form equation, I think we should be able to do it without any effort!

Let me talk to my collaborators if we find a couple hours free time.

## Review with good friends top tribologists, including Muser

Modeling and simulation in tribology across scales: An overview

http://imechanica.org/node/22143

## in the case of larger adhesion, the problem is interesting

The contact challenge was devised in the not very interesting case where there is extremely low adhesion, with no stickiness and no pull-off.

A more interesting and "challenging" problem (perhaps worth a contact challenge 2.0), is the case with significant adhesion.

Recently, I derived an approximate, but simple closed form result, see here. Previously I had developed a BAM model, so the number of models start to be significant, with the ones I propose being also simple equations, whereas I have not had time to implement the very complicated Persson's proposals.