Abstract
Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rateandstate friction law which leads to a mathematically wellposed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stickslip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a twoparameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rateandstate laws, is required in order to capture the full richness of wave types.
Original language  English 

Article number  0606 
Pages (fromto)  1  27 
Number of pages  27 
Journal  Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences 
Volume  473 
Issue number  2203 
Early online date  5 Jul 2017 
DOIs  
Publication status  Published  31 Jul 2017 
Keywords
 Detachment front
 Friction
 Global bifurcation
 Rateandstate
 Selfhealing slip pulse
ASJC Scopus subject areas
 Mathematics(all)
 Engineering(all)
 Physics and Astronomy(all)
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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 Policy Research (IPR)
 Water Informatics: Science and Engineering Centre for Doctoral Training (WISE)
 Centre for Mathematical Biology
Person: Research & Teaching