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

TL;DR

This paper introduces a generalized time-evolution model for contact problems with wear, incorporating non-local time dependence, fractional calculus, and variable load, with analysis and numerical illustration.

Contribution

It extends classical models by integrating fractional calculus and non-local effects to better capture wear dynamics under variable loads.

Findings

Model successfully incorporates non-local time dependence and fractional calculus.

Numerical results demonstrate the model's applicability and accuracy.

Comparison shows improvements over traditional contact wear models.

Abstract

In this paper, we revisit some classical and recent works on modelling slide-contact with wear and propose their generalisation. Namely, we upgrade the relation between the pressure and the wear rate by incorporating some non-local 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 comparison with similar models is discussed.