Stable and unstable development of an interfacial sliding instability

Area of Science:

• Solid Mechanics
• Nonlinear Dynamics
• Friction and Wear

Background:

• Frictional interfaces in elastic bodies are fundamental to many mechanical systems.
• Understanding the stability of sliding rates is crucial for predicting system behavior.
• Laboratory-constrained frictional relations may not universally scale to all configurations.

Purpose of the Study:

• To investigate nonlinear instabilities in the sliding rate of frictional interfaces.
• To determine if simple configurations exhibit universal scaling laws in friction.
• To explore the transition from stable to chaotic dynamics in elastic friction.

Main Methods:

• Solving an equivalent classical problem in fracture mechanics to find blowup solutions.
• Analyzing the stability of these solutions as fixed points of a dynamical system.
• Investigating the effect of a single parameter on stability loss via Hopf bifurcations.

Main Results:

• Identified blowup solutions for the nonlinear instability of sliding rate.
• Demonstrated that solution stability is lost through a cascade of Hopf bifurcations.
• Observed the emergence of chaotic dynamics as a parameter increases.

Conclusions:

• Nonlinear instabilities can lead to chaotic dynamics even in simple frictional systems.
• The transition to chaos is driven by bifurcations in the dynamical system.
• Findings challenge assumptions of universal scaling in laboratory-constrained friction models.