A comparative study between Amontons-Coulomb and Dieterich-Ruina friction laws for the cyclic response of a single degree of freedom system

Alessandro Cabboi*, Luca Marino, Alice Cicirello

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

This study aims at assessing the predictive performance of the Amontons–Coulomb law to reliably predict the cyclic response, inclusive of stick–slip, of a single degree of freedom system in contact with the ground through two versions (steady-state and rate-and-state) of a regularized Dieterich–Ruina law. The assessment is carried out by defining a cost function and a physics-based constraint that enable the identification of the corresponding optimal coefficients of the Amontons–Coulomb law through a multi-start constrained non-linear optimization. The comparative study starts with a sensitivity analysis, aimed at first identifying the most meaningful model parameters for the Dieterich–Ruina law. Subsequently, the cyclic dynamic responses provided by both friction laws are analysed for varying model parameters, and characteristic features are observed within the dynamic forcing–displacement graph and the friction force–velocity plot, that could be directly linked to one friction model or the other. The sensitivity analysis led to the definition of a cost function expressed in terms of the displacement and velocity response differences and a constraint based on the phase difference. The optimization study identified areas of the Dieterich–Ruina's parameter space for which the Amontons–Coulomb law can reliably be used to predict a cyclic stick–slip response. The relevance of these results with respect to problems of modelling and identification of friction are discussed.

Original languageEnglish
Article number104737
Number of pages18
JournalEuropean Journal of Mechanics A - Solids
Volume96
DOIs
Publication statusPublished - 2022

Keywords

  • Stick–slip
  • Nonlinear vibration
  • Constitutive friction laws
  • Rate-and-state laws

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