Organisers

• Alberto Petri (CNR - Istituto dei Sistemi Complessi, Roma, Italy)
• Andrea Vanossi (International School for Advanced Studies (SISSA), Trieste, Italy)
• Michael Urbakh (School of Chemistry, Tel Aviv University, Israel)

Supports

   CECAM

Description

Between microscopic and continuum length scales, meso-scale phenomena are fundamental in understanding shear between material interfaces, and can be considered as the bridge between the two length scales for studying material response. A huge amount of experimental and theoretical work has been devoted to modeling and understanding the properties of microscopic defects but the question of how microstructural properties link to the macroscopic constitutive equations of continuum mechanics is crucial and poorly understood. Often the transition from discrete defects to continuum mechanics is accomplished by simple homogenization procedures neglecting the complex features of the process, employing tools of continuum mechanics to model deformations and slip, e.g., in the crust during earthquakes, as well as the rheology of snow avalanches and landslides. However the presence at the meso-scale of many structural elements like surface roughness, grains, fluid films, different material mixtures, and of their combined effects in determining the system response, make the problem of bridging the associated length scales very complex.

Computer simulations are powerful theoretical tools to study frictional phenomena at so many different length scales; they allow controlled numerical “experiments” where the geometry, sliding conditions and interactions between the constitutive parts (whether atoms or macroscopic grains) can be varied at will, and where the full dynamics of the system can be followed, unlike in real laboratory experiments or in nature. Thanks to the computational resources available nowadays, it is often possible to carry out numerical simulations of system sizes approaching those of real physical interest, albeit not always on the appropriate time scales.

Different models and computational techniques are employed to mimic and finally understand interfacial processes from nano up to the macroscale:

1) We can consider simple, “minimalistic” models, which are based on simplified interaction potentials and focus only on the most relevant degrees of freedom of the system, trying to retain the most important features. In spite of their simplicity these models can explain phenomena of high complexity and have contributed to unravel some important concepts of the mechanisms of friction (e.g., the role of commensurability of the contacting surfaces, the transition from intermittent stick-slip to smooth sliding, the onset of sliding motion, the mechanisms of detachment fronts preceding overall macroscopic sliding, the scaling laws describing statistics of earthquakes, some aspects of the creeping-to-sliding transition in fault like mechanics). 

2) A different kind of simplified approach which allows to connect  microscopic and   meso-macroscopic scales consists in the inclusion of suitable noise terms in otherwise homogeneous equations. Recent results show that this approach is  successful in effectively  describing  intermittency and fluctuations often observed in experiments. 

3)  Another possible approach is via extensive molecular dynamics simulations with more realistic interaction potentials and geometries. This route is usually taken to understand intricate processes such as, for example, wear and plastic deformations in the contact of sliding solid surfaces. The time and length scales for a truly realistic approach are still beyond reach and the computer simulations still rather heavy. An important issue, therefore, is how to reduce the large-scale, many-parameter MD simulations to simpler descriptions with only a few equations of motion.

4) An additional understanding of friction phenomena come from phenomenological Rate-State (RS) models that have been used to describe a wide range of observed frictional behaviors, such as the dilation of a liquid under shear and the transition between stick–slip (regular or chaotic) and smooth sliding friction. However, most “state variables” in RS models cannot yet be quantitatively related to physical system properties, and the main challenge is to define these variables starting from a microscopic description. 

Each of these methods has its strengths and weaknesses. Large-scale simulations allow to reproduce quite accurately some experimental features, but are not really well suited to extract general information at a fundamental level; Rate-State models capture many experimental features quantitatively, but the physical nature of the state variable is unspecified, not allowing to fully rationalize the results of observations; minimalistic models have the advantage of being computationally cheap and simple enough to enable us to work out the general mechanisms at play of the problem, but, obviously, they are not system specific.

Scientific Objectives

The goal of the workshop is to develop new interdisciplinary directions and to discuss how different approaches can be efficiently combined and to which extent new algorithms can reliably bridge the micro and macroscopic time and length scales of the simulations in frictional phenomena from atomic scale processes to seismic events. No doubt that recent advances by researchers in physics, mechanics, materials science, seismology and geophysics are not often communicated across disciplines. As an example, statistical approaches seem at present limited to the tectonic scale, since there intermittence and fluctuations take place at human time and length scales. It seems therefore that scarcity of statistical investigations of friction and grain dynamics is due to pure anthropological reasons. The ideal size of this focused meeting offers indeed an excellent occasion to encourage connections between different groups working on interrelated and complementary issues.

It’s important here to stress some computational issues that will be addressed during the workshop:

1) The proper choice of the interaction potential for a given system has to be unravelled: the complexity of this interactions ranges from simple 2-body semiempirical potentials to more complicated many-body Brenner-like model potentials, taking into account bond-stretching, bending and torsional energies.

2) Effective algorithms that bridge the microscopic time scales of the simulations to the macroscopic time scales of the experiments are required. At the microscopic scales, this is, e.g., connected to a multiscale problem in AFM: the slow dynamics of the massive cantilever in comparison with the fast dynamics of atoms in contact region. How can we provide a bridge between so different time scales in a unifying approach?

3) Development of numerical and theoretical approaches to model dynamics in multicontact systems and to bridge between descriptions of single contact, discrete arrays and extended systems.

4) Development of a multiscale approach, which combines Molecular Dynamics simulations with larger scale ‘continuum-like’ descriptions, to model dry and lubricated friction at macro-scales. Derivation of constitutive relations, and development of mean-field type description for simulations of friction processes at time scales and length scales relevant to experimental conditions.

5)  Inclusion of suitable noise terms in the description at the macroscopic level. This allows to maintain mean-field type descriptions while taking into account the effect of heterogeneities and defects of various kind that in certain situations make homogeneisation techniques ineffective. The actual form and properties of these terms, as appearing at the macroscopic scales, are presently empirically determined from the experiments. The aim is to derive them on the base of  Molecular Dynamics simulations.

6) Statistical analysis of stick-slip events (amplitudes, slip durations) at nano and macro-scales and derivation may lead to understanding an origin of the scaling laws which have a great importance in the geophysical area. Such analysis will allow to define the key parameters for the scaling laws, and their dependencies on external parameters, such as the temperature and material properties. 

The workshop is planned to have ca 20 talks distributed over three days. These talks are intended to give an overview on a particular topic and thereby stimulate discussions. The talks are scheduled to be 30 minutes long and 10 minutes are reserved for discussion after each talk. These talks will be divided into thematic sessions and each session will have a general discussion at the end. 

References

[1] M. Urbakh, J. Klafter, D. Gourdon, and J. Israelachvili The nonlinear nature of friction, Nature 430 525 (2004).
[2] O.M. Braun and A.G. Naumovets Nanotribology: Microscopic mechanisms of friction, Surface Science Reports 60 79 (2006).
[3] A. Socoliuc, E. Gnecco, S. Maier, O. Pfeiffer, A. Baratoff, R. Bennewitz, and E. Meyer Atomic-Scale Control of Friction by Actuation of Nanometer-Sized Contacts, Science 313 207 (2006).
[4] R. W. Carpick Controlling Friction, Science 313 184 (2006).
[5] A. Socoliuc, R. Bennewitz, E. Gnecco, and E. Meyer Transition from Stick-slip to Continuous Sliding in Atomic Friction: Entering a New Regime of Ultralow Friction, Phys. Rev. Lett. 92 134301 (2004).
[6] M. Dienwiebel, G.S. Verhoeven, N. Pradeep, J.W.M Frenken, J.A. Heimberg, and H.W. Zandbergen Superlubricity of Graphite, Phys. Rev. Lett. 92 126101 (2004).
[7] A.E. Filippov, M. Dienwiebel, J.W.M. Frenken, J. Klafter, and M. Urbakh Torque and Twist against Superlubricity, Phys. Rev. Lett. 100 046102 (2008).
[8] M. Evstigneev and P. Reimann Rate description of the stick-slip motion in friction force microscopy experiments, Phys. Rev. E 71 056119 (2005).
[9] P. Reimann and M. Evstigneev Nonmonotonic velocity dependence of atomic friction, Phys. Rev. Lett. 93 230802 (2004).
[10] O.M. Braun, A. Vanossi, and E. Tosatti Incommensurability of a confined system under shear, Phys. Rev. Lett. 95 026102 (2005).
[11] A. Baldassarri, F. Dalton, A. Petri, S. Zapperi, G. Pontuale, and L. Pietronero Brownian Forces in Sheared Granular Matter, Phys. Rev. Lett. 96 118002 (2006).
[12] F. Dalton, F. Farrelly, A. Petri, L. Pietronero, L. Pitolli, and G. Pontuale Shear Stress Fluctuations in the Granular Liquid and Solid Phases, Phys. Rev. Lett. 95 138001 (2005).
[13] P.A. Thompson and M.O. Robbins Origin of stick-slip motion in boundary lubrication, Science 250 792 (1990).
[14] M.H. Muser, M. Urbakh, and M.O. Robbins Statistical mechanics of static and low-velocity kinetic friction, Advances in Chemical Physics 126 187 (2003).
[15] R. Capozza, A. Vanossi, A. Vezzani, and S. Zapperi Suppression of Friction by Mechanical Vibrations, Phys. Rev. Lett. (2009) in press.
[16] S.M. Rubinstein, G. Cohen, and J. Fineberg Detachment fronts and the onset of dynamic friction, Nature 430 1005 (2004).
[17] R.R. Hartley and R.P. Behringer Logarithmic rate dependence of force networks in sheared granular materials, Nature 421 928 (2003).
[18] C. Marone The effect of loading rate on static friction and the rate of fault healing during the earthquake cycle, Nature 391 69 (1998).
[19] P. Johnson, H. Savage, M. Knuth, J. Gomberg, and C. Marone Effects of acoustic waves on stick–slip in granular media and implications for earthquakes, Nature 451 57 (2008).
[20] E. Aharonov and D. Sparks Stick-slip motion in simulated granular layers, J. Geophys. Res. 109 B09306 (2004).
[21] F. Csikor, C. Motz, D. Weygand, M. Zaiser, and S. Zapperi Dislocation Avalanches, Strain Bursts,and the Problem of Plastic Forming at the Micrometer Scale, Science 318 251 (2007).
[22] B. Luan and M.O. Robbins The breakdown of continuum models for mechanical contacts, Nature 435 929 (2005).