Frontiers of Contact Mechanics: A Challenge to Experimentalists in the Study of Friction, Plasticity, and Adhesion

Three requests for experimental collaboration: (i) static friction coefficient depends on geometry! (ii) load-indentation curves in elasto plastic materials with roughness and (iii) adhesion of layered materials in the presence of roughness.
M.Ciavarella. Politecnico di BARI, Italy. [email protected]

1) Inspired by beautiful experiments of Jay Fineberg and also of Bart Weber and recent concepts in friction that are mainly used in geophysics and initiated by the great Jim Rice from Harvard (slip-weakening friction, fracture cohesive models of friction), I wrote a short note with a very nice young guy from Singapore (Shubo Zhang) on how geometry seems to affect static friction coefficient. Any comment is welcome since paper is just submitted.
https://www.researchgate.net/publication/393786851_Static_friction_coefficient_depends_on_geometry
The Griffith theory for fracture, which was developed for 3D Hertz contact by Ciavarella (JMPS, 2015), postulates a fixed dynamic friction coefficient (reached at heavy loads), but a static friction coefficient which we demonstrate depends largely on geometry. In particular, by considering the pressure dependence of the friction fracture energy, the friction coefficients ratio at small normal loads tends to a limit which for a power law profile depends only on the power law exponent. Flatter profiles therefore are predicted to have very wide range of friction ratios, which may explain why scattered values has been reported.
However, to explore the full dependence on the load, Bart Weber with spheres had to recur to 3 decades of change in normal load (more details at https://arxiv.org/pdf/2409.04280 which I invite to study also for experimental setup).
It would be great if we could test the above theory about flatter geometries. Naturally, this introduces some experimental additional challenge with respect to the sphere case because of more difficult alignment — Jay Fineberg already demonstrated that a change in alignment for a perfectly flat rectangular block changes friction coefficient by a significant amount, which per se is another convincing evidence for Griffith friction theory, although for perfectly flat geometries the halfspace model does not work and one cannot obtain analytical results. Hence, a cubic, quartic profiles would be interesting. But even the flat profile could be interesting, as long as we test a wide range of normal loads, which is not explored so far by Fineberg.
Who could be interested to embark into an experimental program to investigate this Griffith theory of friction, the geometrical / normal load / size effect dependence of friction coefficient? It sounds an exciting and fundamental problem in friction, spanning applications from engineering, to earthquakes mechanics etc. Indeed, many engineers still use the rather crude Amonton-Coulomb model for friction, and this may well be a mistake.
I am of course available for any discussion.

2) Please find enclosed a new paper result of very long work with modelling elasto-plastic rough contacts. We find for the first time load indentation curves with the “constant hardness” model, and we find universal results which generalize the Persson’s model to much greater validity. The analytical load indentation curve can of course be differentiated to give results in terms of macroscopic stiffness. This will result in stiffness being proportional to load, but we also give complete results about prefactors. It would be nice to test these results with experiments!

3) Please find enclosed a new fully analytical theory for (long range) adhesive contact of a solid with a soft layer on top, with a rigid surface, obtained with the Bearing Area Model of Ciavarella. This gives a simple analytical solution to the full contact problem, and not just the prediction of pull-off as Persson-Tosatti one. Comparison between the new theory and Persson-Tosatti are given, showing there is a region where there are significant discrepancies: unfortunately detailed experimental assessment is not available (there are however experiments by the group of Bo Persson in a reference given in the paper, but perhaps this is too limited data), so if anyone is interested, please we are very interested! Any comment is welcome.