### 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 rate-and-state friction law which leads to a mathematically well-posed 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 stick-slip 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 two-parameter 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 rate-and-state laws, is required in order to capture the full richness of wave types.

Original language | English |
---|---|

Article number | 0606 |

Pages (from-to) | 1 - 27 |

Number of pages | 27 |

Journal | Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences |

Volume | 473 |

Issue number | 2203 |

DOIs | |

Publication status | Published - 5 Jul 2017 |

### Fingerprint

### Keywords

- Detachment front
- Friction
- Global bifurcation
- Rate-and-state
- Self-healing slip pulse

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

### Cite this

*Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences*,

*473*(2203), 1 - 27. [0606]. https://doi.org/10.1098/rspa.2016.0606

**A phase-plane analysis of localized frictional waves.** / Putelat, T; Dawes, J. H.P.; Champneys, A R.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences*, vol. 473, no. 2203, 0606, pp. 1 - 27. https://doi.org/10.1098/rspa.2016.0606

}

TY - JOUR

T1 - A phase-plane analysis of localized frictional waves

AU - Putelat, T

AU - Dawes, J. H.P.

AU - Champneys, A R

PY - 2017/7/5

Y1 - 2017/7/5

N2 - 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 rate-and-state friction law which leads to a mathematically well-posed 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 stick-slip 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 two-parameter 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 rate-and-state laws, is required in order to capture the full richness of wave types.

AB - 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 rate-and-state friction law which leads to a mathematically well-posed 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 stick-slip 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 two-parameter 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 rate-and-state laws, is required in order to capture the full richness of wave types.

KW - Detachment front

KW - Friction

KW - Global bifurcation

KW - Rate-and-state

KW - Self-healing slip pulse

UR - http://www.scopus.com/inward/record.url?scp=85026637946&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1098/rspa.2016.0606

U2 - 10.1098/rspa.2016.0606

DO - 10.1098/rspa.2016.0606

M3 - Article

VL - 473

SP - 1

EP - 27

JO - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences

SN - 1364-503X

IS - 2203

M1 - 0606

ER -