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Viscoelastic toy model explaining the static friction paradox in stick-slip instability without friction laws

Toshiki Watanabe and Ken Nakano*

  • *Contact author: nakano@ynu.ac.jp
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Phys. Rev. E 111, 065504 – Published 18 June, 2025

DOI: https://doi.org/10.1103/dn4g-chy7

Abstract

The relaxation oscillation in sliding systems is termed stick-slip (SS) since the two surfaces in contact seem to repeat the stick and slip states. However, several precise measurements have revealed that extremely slow slip occurs in even apparently stick states before every stick-to-slip transition, which is here termed the static friction paradox. This study theoretically investigates instabilities induced by solid viscoelasticity using a minimal toy model without friction laws: a two-degrees-of-freedom sliding system consisting of a rigid probe and a Kelvin-Voigt viscoelastic foundation (VEF). Taking advantage of its simplicity, we discuss the mechanisms generating various system dynamics based on stability analysis and numerical simulation. As a result, surprisingly, even though the sliding system does not employ static friction, it exhibits intermittent oscillation resembling the typical SS instability. It comprises two slip states for the contact between the probe and the VEF, i.e., slow-slip and fast-slip states, providing a purely mechanical explanation for the static friction paradox.

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Phys. Rev. E 111, 065504– Published 18 June, 2025
  • Received 10 December 2024
  • Revised 5 May 2025
  • Accepted 19 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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