Relaxation of Sliding Friction from a Statistical Model of Aging Contacts
Ryudo Suzuki
Abstract
Frictional relaxation after a sudden velocity change underlies the phenomenological laws that describe the stability of steady sliding and of seismic faults. To connect this relaxation with measurable statistics of microscopic contacts, we introduce a minimal model incorporating logarithmic aging of contact forces and a power-law contact-size distribution reflecting fractal interface roughness, and derive the relaxation function analytically. Depending on the power-law exponent α, the intermediate-time response exhibits a plateau, logarithmic decay, or power-law decay, in contrast to the exponential decay assumed in the phenomenological laws. The theory provides experimentally testable links between microscopic contact statistics and macroscopic frictional relaxation.
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