Variational and numerical analysis of a dynamic viscoelastic contact problem with friction and wear

ABSTRACT

In this paper, we consider a dynamic viscoelastic contact problem with friction and wear, and describe it as a system of nonlinear partial differential equations. We formulate the previous problem as a hyperbolic quasi-variational inequality by employing the variational method. We adopt the Rothe method to show the existence and uniqueness of solution for the hyperbolic quasi-variational inequality under mild conditions. We also give a fully discrete scheme for solving the hyperbolic quasi-variational inequality and obtain error estimates for the fully discrete scheme.

Keywords:

• Viscoelastic contact
• frictional contact
• hyperbolic quasi-variational inequality
• fully discrete scheme
• error estimate

2010 AMS Subject Classifications:

• 74M15
• 74M10
• 49J40
• 74G25
• 74G30
• 65N30

Acknowledgments

The authors are grateful to Professor M. Sofonea for his valuable comments and suggestions. We also thank the editor and reviewers for their constructive comments, which helps us to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 11471230, 11671282, 11771067] and the Applied Basic Project of Sichuan Province [grant number 2019YJ0204].