Fully history-dependent quasivariational inequalities in contact mechanics

Abstract

In this paper, we consider a new class of fully history-dependent quasivariational inequalities which arise in the study of quasistatic models of contact and involve two history-dependent operators. By using a fixed-point theorem and arguments of monotonicity and convexity, we prove an existence and uniqueness result of the solution, which includes as special cases some results already obtained in some papers. Then, the obtained result is applied to two problems of quasistatic frictional contact for viscoelastic materials and the unique weak solvability of each contact problem is obtained.

Keywords:

• Fully history-dependent quasivariational inequalities
• existence and uniqueness
• fixed-point theorem
• quasistatic frictional contact
• viscoelastic materials

AMS Subject Classifications:

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

Notes

The authors declare that they have no conflict of interest.

Additional information

Funding

This work of the second author was supported by the National Natural Science Foundation of China [grant number 81171411]; the China Postdoctoral Science Foundation [grant number 2014M552328, 2015T80967]; the Postdoctoral Science Foundation of Sichuan Province, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.