The paper by Rice and Ruina investigates the stability of steady frictional slipping in mechanical systems. They analyze the conditions under which steady sliding remains stable or becomes unstable, considering the dependence of frictional stress on slip rate and the evolving state of the surface. The frictional stress is modeled as a function of both slip rate $ V $ and the state of the surface, which evolves with ongoing slip. This state-dependent frictional behavior is contrasted with classical models that assume friction is only a function of slip rate.
For a single-degree-of-freedom elastic system, the paper shows that instability occurs when the spring stiffness (or appropriate viscoelastic generalization) reaches a critical value, leading to flutter oscillations. The critical stiffness is determined by the properties of the friction law, including the instantaneous viscosity and the long-term decay of the frictional stress. The analysis also shows that increases in inertia of the slipping system are destabilizing, as they increase the critical stiffness required for stability.
The paper extends these findings to slipping continua with spatially periodic perturbations along their interface, where propagating frictional creep waves are established at critical conditions. The analysis also considers viscoelastic effects, showing that the critical stiffness depends on the viscoelastic properties of the system.
The paper concludes that the steady-state frictional stress is a decreasing function of slip rate, which is a necessary condition for the instability of steady sliding. The results are supported by experimental observations and theoretical models, and the analysis is applied to both elastic and viscoelastic systems. The paper also discusses the implications of these findings for the understanding of fault slip and other mechanical systems involving frictional sliding.The paper by Rice and Ruina investigates the stability of steady frictional slipping in mechanical systems. They analyze the conditions under which steady sliding remains stable or becomes unstable, considering the dependence of frictional stress on slip rate and the evolving state of the surface. The frictional stress is modeled as a function of both slip rate $ V $ and the state of the surface, which evolves with ongoing slip. This state-dependent frictional behavior is contrasted with classical models that assume friction is only a function of slip rate.
For a single-degree-of-freedom elastic system, the paper shows that instability occurs when the spring stiffness (or appropriate viscoelastic generalization) reaches a critical value, leading to flutter oscillations. The critical stiffness is determined by the properties of the friction law, including the instantaneous viscosity and the long-term decay of the frictional stress. The analysis also shows that increases in inertia of the slipping system are destabilizing, as they increase the critical stiffness required for stability.
The paper extends these findings to slipping continua with spatially periodic perturbations along their interface, where propagating frictional creep waves are established at critical conditions. The analysis also considers viscoelastic effects, showing that the critical stiffness depends on the viscoelastic properties of the system.
The paper concludes that the steady-state frictional stress is a decreasing function of slip rate, which is a necessary condition for the instability of steady sliding. The results are supported by experimental observations and theoretical models, and the analysis is applied to both elastic and viscoelastic systems. The paper also discusses the implications of these findings for the understanding of fault slip and other mechanical systems involving frictional sliding.