Abstract
The physics of dry friction is often modelled by assuming that static and kinetic frictional forces can be represented by a pair of coefficients usually referred to as μ_{s} and μ_{k}, respectively. In this paper we reexamine this discontinuous dichotomy and relate it quantitatively to the more general, and smooth, framework of rateandstate friction. This is important because it enables us to link the ideas behind the widely used static and dynamic coefficients to the more complex concepts that lie behind the rateandstate framework. Further, we introduce a generic framework for rateandstate friction that unifies different approaches found in the literature. We consider specific dynamical models for the motion of a rigid block sliding on an inclined surface. In the Coulomb model with constant dynamic friction coefficient, sliding at constant velocity is not possible. In the rateandstate formalism steady sliding states exist, and analysing their existence and stability enables us to show that the static friction coefficient μ_{s} should be interpreted as the local maximum at very small slip rates of the steady state rateandstate friction law. Next, we revisit the oftencited experiments of Rabinowicz (J. Appl. Phys., 22:13731379, 1951). Rabinowicz further developed the idea of static and kinetic friction by proposing that the friction coefficient maintains its higher and static value μ_{s} over a persistence length before dropping to the value μ_{k}. We show that there is a natural identification of the persistence length with the distance that the block slips as measured along the stable manifold of the saddle point equilibrium in the phase space of the rateandstate dynamics. This enables us explicitly to define μ_{s} in terms of the rateandstate variables and hence link Rabinowicz's ideas to rateandstate friction laws. This stable manifold naturally separates two basins of attraction in the phase space: initial conditions in the first one lead to the block eventually stopping, while in the second basin of attraction the sliding motion continues indefinitely. We show that a second definition of μ_{s} is possible, compatible with the first one, as the weighted average of the rateandstate friction coefficient over the time the block is in motion.
Original language  English 

Pages (fromto)  7093 
Number of pages  24 
Journal  Journal of the Mechanics and Physics of Solids 
Volume  78 
Early online date  2 Feb 2015 
DOIs  
Publication status  Published  1 May 2015 
Keywords
 Bistability
 Friction angle
 Landslide
 Nonmonotonic friction
 Slope stability
 Stickslip
 Stiction loss
ASJC Scopus subject areas
 Condensed Matter Physics
 Mechanics of Materials
 Mechanical Engineering
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Profiles

Jonathan Dawes
 Department of Mathematical Sciences  Professor
 Centre for Networks and Collective Behaviour
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
 Water Innovation and Research Centre (WIRC)
 Institute for Mathematical Innovation (IMI)
 Institute for Policy Research (IPR)
 Water Informatics: Science and Engineering Centre for Doctoral Training (WISE)
 Centre for Mathematical Biology
Person: Research & Teaching