A unilateral constraint contact problem for viscoelastic materials with wear

Abstract

The aim of this work is to investigate a mathematical model that describes the frictional contact between viscoelastic materials with a long memory and a moving foundation. The contact condition is modeled with a version of normal compliance condition with unilateral constraint in which wear of foundation is considered. Friction contact condition follows a sliding version of Coulomb's law of dry friction. We derive a variational formulation of the problem, which couples a variational inequality and an integral equation. Then, we obtain the unique weak solvability of the contact problem by virtue of a fixed point theorem. By using the penalization method, we discuss the convergence of the contact problem. Further, we obtain the unique solution of the penalized problem and this solution converges to the solution of the original contact model as the penalization parameter converges to zero.

Keywords:

• Viscoelastic materials
• unilateral constraint
• wear
• existence and uniqueness
• normal compliance

2010 Mathematics Subject Classifications:

• 74M10
• 74M15
• 49J40
• 74G30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [grant numbers 12161015, 12001120], Training Object of High Level and Innovative Talents of Guizhou Province [grant number (2016)4006], Guizhou Data Driven Modeling Learning and Optimization Innovation Team [grant number [2020]5016], and the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi [grant number 2020L0470].