Variational analysis and numerical simulation for a dynamic contact problem with Coulomb’s friction in thermo-viscoelasticity
Abstract
The focus of this study is a dynamic frictional contact model involving a viscoelastic body with thermal effects and a conductive foundation.Coulomb's law describes the frictional behavior, while a normal compliance model simulates the contact.We derive a variational formulation for the problem and establish the existence of a unique weak solution by using the Banach fixed point theorem.To solve the problem, we propose a fully discrete scheme that combines the finite element method for spatial approximation with the Euler scheme for the time discretization.Error estimates for the solutions are derived, and linear convergence is achieved under suitable regularity assumptions.Finally, numerical simulations are presented to demonstrate the performance of the proposed method.
Fields of Study & Subjects
Contact Mechanics and Variational Inequalities
Adhesion
Friction
and Surface Interactions
Brake Systems and Friction Analysis
Publication details
- Journal / source
- Applied Set-Valued Analysis and Optimization
- Publisher
- Mathematical Research Press
- Volume
- 8
- Issue
- 2
- Pages
- 147–166
- Publication date
- 17 January 2026