A new class of fully history-dependent variational-hemivariational inequalities with application to contact mechanics

Abstract

In this paper, we consider the behaviour of solutions to a class of fully history-dependent variational-hemivariational inequalities with respect to the perturbation of the data. First, the existence and uniqueness of the solution to a class of fully history-dependent variational-hemivariational inequalities is obtained by using a fixed point theorem. Second, we obtain continuous dependence result of solutions with respect to all the data of variational-hemivariational inequalities. Meanwhile, the convergence results of the solutions for the special case of abstract variational inequalities are also given. Finally, to illustrate our main results, we consider a class of viscoelastic contact problem with a long memory. By using our abstract result, we get the continuous dependence of the solutions to frictional contact problem with respect to all the data.

Keywords:

• Full history-dependent
• variational-hemivariational inequalities
• unilateral constraint
• convergence
• frictional contact problem

MSC 2010:

• 49J40
• 74H20
• 74H25
• 74M10
• 74M15

Acknowledgments

The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too. Furi Guo, JinRong Wang and Liang Lu: Writing-original draft; Writing-review and editing. JinRong Wang: Supervision.

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 number 12161015], Qian Ke He Ping Tai Ren Cai-YSZ[2022]002, Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), Guangxi Natural Science Foundation (2021GXNSFAA075022) and the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi [grant number 2021L0382].