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Mathematical Problems in Engineering
Volume 2012, Article ID 396745, 22 pages
Research Article

A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time Delay

1Department of Mathematics, Sichuan University, Chengdu 610064, China
2Department of Mathematics, Kunming University, Kunming 650221, China

Received 27 June 2012; Revised 26 September 2012; Accepted 16 November 2012

Academic Editor: Marco Paggi

Copyright © 2012 Si-sheng Yao and Nan-jing Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A mathematical model which describes an explicit time-dependent quasistatic frictional contact problem between a deformable body and a foundation is introduced and studied, in which the contact is bilateral, the friction is modeled with Tresca’s friction law with the friction bound depending on the total slip, and the behavior of the material is described with a viscoelastic constitutive law with time delay. The variational formulation of the mathematical model is given as a quasistatic integro-differential variational inequality system. Based on arguments of the time-dependent variational inequality and Banach's fixed point theorem, an existence and uniqueness of the solution for the quasistatic integro-differential variational inequality system is proved under some suitable conditions. Furthermore, the behavior of the solution with respect to perturbations of time-delay term is considered and a convergence result is also given.