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A generalised time-evolution model for contact problems with wear and its analysis

Dmitry Ponomarev

Vol. 10 (2022), No. 3, 279–319
Abstract

We revisit some classical and recent works on modelling sliding contact with wear and propose their generalisation. Namely, we upgrade the relation between the pressure and the wear rate by incorporating some nonlocal time-dependence. To this effect, we use a combination of fractional calculus and relaxation effects. Moreover, we consider a possibility when the load is not constant in time. The proposed model is analysed and solved. The results are illustrated numerically and comparisons with similar models are discussed.

Keywords
contact problems, punch motion with a constant speed, wear of material, fractional order models
Mathematical Subject Classification
Primary: 26A33, 45A05, 45B05, 45M05, 45P05
Milestones
Received: 17 March 2022
Revised: 7 September 2022
Accepted: 10 October 2022
Published: 4 December 2022

Communicated by Emilio Barchiesi
Authors
Dmitry Ponomarev
FACTAS Team
Centre Inria d’Université Côte d’Azur
Biot
France
St. Petersburg Department
Steklov Mathematical Institute
Russian Academy of Sciences
St. Petersburg
Russia