A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time Delay
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...
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2012/396745 |
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doaj-c3b8305d07ec4265a657c46b955e78592020-11-24T23:00:46ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472012-01-01201210.1155/2012/396745396745A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time DelaySi-sheng Yao0Nan-jing Huang1Department of Mathematics, Sichuan University, Chengdu 610064, ChinaDepartment of Mathematics, Sichuan University, Chengdu 610064, ChinaA 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.http://dx.doi.org/10.1155/2012/396745 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Si-sheng Yao Nan-jing Huang |
spellingShingle |
Si-sheng Yao Nan-jing Huang A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time Delay Mathematical Problems in Engineering |
author_facet |
Si-sheng Yao Nan-jing Huang |
author_sort |
Si-sheng Yao |
title |
A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time Delay |
title_short |
A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time Delay |
title_full |
A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time Delay |
title_fullStr |
A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time Delay |
title_full_unstemmed |
A Quasistatic Contact Problem for Viscoelastic Materials with Slip-Dependent Friction and Time Delay |
title_sort |
quasistatic contact problem for viscoelastic materials with slip-dependent friction and time delay |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
2012-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2012/396745 |
work_keys_str_mv |
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