TY - JOUR

T1 - A comparative study between Amontons-Coulomb and Dieterich-Ruina friction laws for the cyclic response of a single degree of freedom system

AU - Cabboi, Alessandro

AU - Marino, Luca

AU - Cicirello, Alice

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Stick–slip

KW - Nonlinear vibration

KW - Constitutive friction laws

KW - Rate-and-state laws

UR - http://www.scopus.com/inward/record.url?scp=85134432568&partnerID=8YFLogxK

U2 - 10.1016/j.euromechsol.2022.104737

DO - 10.1016/j.euromechsol.2022.104737

M3 - Article

VL - 96

JO - European Journal of Mechanics A - Solids

JF - European Journal of Mechanics A - Solids

SN - 0997-7538

M1 - 104737

ER -