Relaxation of Sliding Friction from a Statistical Model of Aging Contacts
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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BibTeX
@misc{suzuki2026relaxation,
title = {{Relaxation of Sliding Friction from a Statistical Model of Aging Contacts}},
author = {Ryudo Suzuki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06998},
eprint = {2609.06998},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06998},
}
RIS
TY - UNPB
TI - Relaxation of Sliding Friction from a Statistical Model of Aging Contacts
AU - Ryudo Suzuki
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06998
UR - https://arxiv.org/abs/2609.06998
AB - 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.
ER -