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

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.