http://www.multiscaleconsulting.com/publications/Contact_mechanics_for_randomly_rough_surfaces.pdf

Contact mechanics for randomly rough surfaces

We study the stability of steady sliding between elastically deformable continua using rate and state dependent friction laws That is done for both elastically identical and elastically dissimilar solids The focus is on linearized response to perturbations of steady-state sliding, and on studying how the positive direct effect (instantaneous increase or decrease of shear strength in response to a respective instantaneous increase or decrease of slip rate) of those laws allows the existence of a quasi-static range of response to perturbations at sufficiently low slip rate We discuss the physical basis of rate and state laws, including the likely basis for the direct effect in thermally activated processes allowing creep slippage at asperity contacts, and estimate activation parameters for quartzite and granite Also, a class of rate and state laws suitable for variable normal stress is presented As part of the work, we show that compromises from the rate and state framework for describing velocity-weakening friction lead to paradoxical results, like supersonic propagation of slip perturbations, or to ill-posedness, when applied to sliding between elastically deformable solids The case of sliding between elastically dissimilar solids has the inherently destabilizing feature that spatially inhomogeneous slip leads to an alteration of normal stress, hence of frictional resistance We show that the rate and state friction laws nevertheless lead to stability of response to sufficiently short wavelength perturbations, at very slow slip rates Further, for slow sliding between dissimilar solids, we show that there is a critical amplitude of velocity-strengthening above which there is stability to perturbations of all wavelengths

http://esag.harvard.edu/rice/197_Rice_Lap_Ranj_JMPS_01.pdf

Rate and state dependent friction and the stability of sliding between elastically deformable solids

We review in this article the current theoretical understanding ofcollective and single particle diA usion on surfaces and how it relates to the existing experimental data. We begin with a brief survey of the experimental techniques that have been employed for the measurement of the surface diA usion coeA cients. This is followed by a section on the basic concepts involved in this ®eld. In particular, we wish to clarify the relation between jump or exchange motion on microscopic length scales, and the diA usion coeA cients which can be de®ned properly only in the long length and time scales. The central role in this is played by the memory eA ects. We also discuss the concept of diA usion under nonequilibrium conditions. In the third section, a variety of diA erent theoretical approaches that have been employed in studying surface diA usion such as ®rst principles calculations, transition state theory, the Langevin equation, Monte Carlo and molecular dynamics simulations, and path integral formalism are presented. These ®rst three sections form an introduction to the ®eld of surface diA usion. Section 4 contains subsections that discuss surface diA usion for various systems which have been investigated both experimentally and theoretically. The focus here is not so much on speci®c systems but rather on important issues concerning diA usion meas

Collective and single particle diÄ usion on surfaces

Friction is a very complicated phenomenon arising at the contact of surfaces. Experiments indicate a functional dependence upon a large variety of parameters, including sliding speed, acceleration, critical sliding distance, temperature, normal load, humidity, surface preparation, and, of course, material combination. In many engineering applications, the success of models in predicting experimental results remains strongly sensitive to the friction model. Furthermore, a broad cross section of engineering and science disciplines have developed interesting ways of representing friction, with models originating from the fundamental mechanics areas, the system dynamics and controls fields, as well as many others. A fundamental unresolved question in system simulation remains: what is the most appropriate way to include friction in an analytical or numerical model, and what are the implications of friction model choice? This review article draws upon the vast body of literature from many diverse engineering fields and critically examines the use of various friction models under different circumstances. Special focus is given to specific topics: lumped-parameter system models !usually of low order"—use of various types of parameter dependence of friction; continuum system models—continuous interface models and their discretization; self-excited system response—steady-sliding stability, stick/slip, and friction model requirements; and forced system response—stick/slip, partial slip, and friction model requirements. The conclusion from this broad survey is that the system model and friction model are fundamentally coupled, and they cannot be chosen independently. Furthermore, the usefulness of friction model and the success of the system dynamic model rely strongly on each other. Across disciplines, it is clear that multi-scale effects can dominate performance of friction contacts, and as a result more research is needed into computational tools and approaches capable of resolving the diverse length scales present in many practical problems. There are 196 references cited in this review-article. #DOI: 10.1115/1.1501080$

Friction modeling for dynamic system simulation

The dynamics of friction have been studied for hundreds of years, yet many aspects of these everyday processes are not understood. One such aspect is the onset of frictional motion (slip). First described more than 200 years ago as the transition from static to dynamic friction, the onset of slip is central to fields as diverse as physics1,2,3, tribology4,5, mechanics of earthquakes6,7,8,9,10,11 and fracture12,13,14. Here we show that the onset of frictional slip is governed by three different types of coherent crack-like fronts: these are observed by real-time visualization of the net contact area that forms the interface separating two blocks of like material. Two of these fronts, which propagate at subsonic and intersonic velocities, have been the subject of intensive recent interest12,13,14,15,16,17. We show that a third type of front, which propagates an order of magnitude more slowly, is the dominant mechanism for the rupture of the interface. No overall motion (sliding) of the blocks occurs until either of the slower two fronts traverses the entire interface.

Detachment fronts and the onset of dynamic friction

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J.J. Shea

Papers

Sliding Friction-Physical Principles and Applications