Papangelo A., Stingl B., Hoffmann N.P., Ciavarella M. / Ôèçè÷åñêàÿ ìåçîìåõàíèêà 17 3 (2014) 98106 98 ÓÄÊ 539.421 A simple model for friction detachment at an interface of finite size mimicking Finebergs experiments on uneven loading A. Papangelo 1 , B. Stingl 2 , N.P. Hoffmann 2,3 , and M. Ciavarella 1 1 Politecnico di Bari, Bari, 70126, Italy 2 Hamburg University of Technology, Hamburg, 21073, Germany 3 Imperial College London, London, SW7 2AZ, UK This work presents a model and simulation results for the friction detachment of a finite sized interface, following previous results on the phenomenon by Ben-David and Fineberg, namely experiments demonstrating that the ratio of shear to normal force needed to move contacting bodies can, instead, vary systematically with controllable changes in the external loading configuration. In particular, we extend a previous one-dimensional simulation model by Bar Sinai with colleagues to a quasi 2D model to allow for a tilting of one of the contacting blocks. While Bar Sinai with colleagues postulate that the presence of slow fronts of detachment (an order of magnitude lower than the usual Rayleigh fronts as in crack propagation) is due to a strengthening term in the friction law, which is not always measured in unlubricated contacts, we find slow fronts also with a purely weakening law. Keywords: sticking to sliding transition, uneven loading, static friction coefficient, slow detachment fronts, velocity strengthening friction © Papangelo A., Stingl B., Hoffmann N.P., Ciavarella M., 2014 1. Introduction The basic laws of dry friction seem simple and have apparently been understood centuries ago by the Italian scientist Leonardo and the French engineers Coulomb and Amontons: the frictional force between two bodies in static contact is proportional to the normal force. The constant of proportionality is called coefficient of (static) friction. This surprisingly simple law, independent on the macro- scopic shape of the body and the apparent area of contact, has been interpreted first by Bowden and Tabor [1] as due to the fact that the contact occurs only on microscopic as- perities and the pressure locally is sufficient to cause yield  friction is therefore due to asperity junction plas- tic failure, and the friction coefficient is the ratio between shear strength and hardness, i.e. about 3 times the yield strength of the softer material (this is the so called plough- ing term, and there can be also an adhesion contribution). Later on, statistical models explained that the average pres- sure on each asperity tends to be constant, and only the number of contacting asperities changes with increasing normal force. Greenwood and Williamson [2] confirmed the proportionality of contact area and normal force with such a statistical approach. Hence, what happens on the asperity scale is crucial to friction. When sliding starts, thermal effects are activated, both at bulk and asperity scales, and this is usually one of the factors called upon to explain the rate-dependence of fric- tion as part of the difference between static and dynamic friction coefficient (see [3]). Yet, for many scopes, the Cou- lomb law is still very much in use, and more complicated laws are often developed empirically trying to account for the influence of other factors, such as speed, normal load, surface conditions, temperature, etc. (see [4]). To summa- rize, while the basic law is still useful for very qualitative results, the understanding of frictional processes is still very far from even remotely completed. Dieterich [5, 6] and Ruina [7] suggested a rate- and state-dependent friction law to explain a large amount of laboratory data on rock friction. The state variable quanti- fies the contact state between sliding surfaces or the inter- nal structure of the gouge layer between sliding surfaces. Various empirical forms exist which consider interface strength as a dynamic entity that is inherently related to both fast processes such as detachment/reattachment, and the slow process of contact area rejuvenation. This can be put as an extension of the BowdenTabor model, which states the solid friction force F needed to slide one solid against the other at relative velocity V reads: F = σΣ, with