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# Lorentz Workshop "Micro/Nano Models for Tribology," Leiden, the Netherlands, 30/1-3/2/2017

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We have organized a Lorentz Workshop with 60 selected partecipants leading scientists in tribology and contact mechanics mainly from Europe.

Attached a program. Or see the web site

Micro/Nanoscale Models for Tribology (μ/n-Tribo-Models)

Vladislav Yastrebov (co-organizer)

Lucia Nicola (co-organizer)

Annalisa Fasolino (co-organizer)

Michele Ciavarella (co-organizer)

Julien Scheibert (co-organizer)

Antonis I. Vakis (co-organizer)

regards, MC

p.s. I removed an introductory provoquative draft "paper" on the relevance of multiscale issues because the two drafts have then converged and evolved into a serious calculation and into a new paper on rubber friction which I have just submitted.

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Lorentz@Oort_2017_Schedule_MC.xls | 102 KB |

Analytical methods.pdf | 124.08 KB |

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## Comments

## an appendix on the "draft paper"

I added an appendix to the draft paper with more details about multiscale paradoxes

"Is Persson rubber friction theory just a complicated and ill-posed fitting equation?"

## a preprint of the simplified Persson's theory

Thinking about the workshop, I have read some literature on rubber friction (on which I knew nothing until end of december), and I have written a note which is in preprint arxiv

https://arxiv.org/abs/1701.03810

There has been some discussion already with Bo Persson who does not admit this finding, but I am simply finding these relatively trivial results

1) the hysteresis loss is essentially dependent on the upper wavenumber cutoff. Unless the fractal dimension of the surface is extremely low, which is not typically the case.

2) this is rather arbitrarily fixed by Persson such that the rms slope is 1.3 --- a "magic universal number"?

3) I find that with even higher slope (which corresponds to nanoscale wavelength) of 3.5, I can fit even results which Persson says "no way can be attributed to hysteresis", and which he has to fit with another contribution to friction, on which he has another 6 different models, all quite complicated (and of course with other fitting constants)

4) the basic finding is essentially the same of Persson 1998 and Popov 2010, so the cumbersome 4 recursive integrals formulation by Persson, and the apparent dependence on the entire PSD spectrum of the surface is confusing.

Any comment?

## another way to look at this result is GW or Pastewka-Robbins

One fundamental reason why Persson's full theory is "single scale" is what found by Pastewka-Robbins (2014), who in turn confirm with a full detailed numerical investigation with no other approximation, a previous qualitative finding of Greenwood-Williamson theories, although these instead suffer from various approximations. The result is that the average diameter of contact spots in a self-affine rough surface contact is independent on load and depends only on small scale geometrical features. In the language of Pastewka-Robbins, d_rep = h'rms/h''rms, where h'rms is the rms slope and h''rms the rms curvature. Since these two quantities are dominated by the truncation wavevumber, already this explains the size of typical asperities is fixed by the truncation wavevector.

Add to this the fact that the various frequencies in the spectrum do NOT contribute equally to the friction coefficient, because typically we refer to the rising part of the curve ImE*(q v)/Abs(E*(q v)) (as otherwise thermal effects introduce many complications. In this case the integration Persson suggests becomes really superflous.

What I find is after all confirmed by very simple theories substantiated with actual experiments see Amino and Uchiyama (2000).

N. Amino and Y. Uchiyama (2000) Relationships Between the Friction and Viscoelastic Properties of Rubber. Tire Science and Technology: July 2000, Vol. 28, No. 3, pp. 178-195. doi: http://dx.doi.org/10.2346/1.2135999. In this study, the relationships between friction and viscoelastic properties such as loss tangent tan δ ′ were examined. Wet skid resistance was measured using the British Pendulum Tester. From the data on wet skid resistance and viscoelastic properties, it is found that the coefficient of friction μ varies as follows: μ = a + b · tan δ/E′

Pastewka, L., & Robbins, M. O. (2014). Contact between rough surfaces and a criterion for macroscopic adhesion.

Proceedings of the National Academy of Sciences,111(9), 3298-3303.Greenwood, J. A., & Williamson, J. B. P. (1966, December). Contact of nominally flat surfaces. In

Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences(Vol. 295, No. 1442, pp. 300-319). The Royal Society## round table progress in analytical methods in contact mechanics

I am about to co-chair the Round Table of this workshop, devoted to Analytical methods: progress and challenges for the next 5-10 years, with Jim Greenwood, emeritus professor of Cambridge University. It is in a form of a question to Jim Greenwood and Jim Barber, who is writing a book in Contact Mechanics.

JimG

do you have an idea of how you want to lead the discussion on the round-table we co-chair next week on "analytical methods"? I basically want to say that Johnson's CM book is 99% of what we know even today, and it is not by chance it has 16 000 citations. I still have my personal copy of 1993 when I was an Erasmus student in Nottingham University, and I don't think I know it all. Maybe JimB has some suggestions on where we have made real progress in analytical methods? I don't see much. Maybe Persson's theory of contact mechanics? It of course gave a cleaner picture of rough contact, but where has it led really of new insight? Not much I think. Maybe Ciavarella-Jager treatment of partial slip and all the variants? Really important? I doubt it. David Hills variants of the asymptotics? I doubt it, Comninou and Dundurs had it all. Perhaps the real progress has been made in adhesion, with all the bio-inspired stuff: KLJ has only 2-3 pages on JKR, whereas nowadays there are tons of papers around. Perhaps viscoelasticity? Of course Carbone has solved numerically problems with many more constants than Hunter solution. But the principle of correspondence was already made. Perhaps rubber friction. The basic ideas were in Grosch 1963. I will also say that you (JimG) were fortunate to work with David Tabor and KLJ, the real fathers of contact mechanics. So I will leave the discussion to you! JimB must have some ideas on where we had some progress, since he is writing an entire book about it! Also, perhaps he knows where to expect real progress in analytical methods?

## I added a small powerpoint for the session on analytical methods

see the main post "analytical methods.pdf"