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Dynamic contact problems with slip-dependent friction in viscoelasticity

100%
Ionescu I. R., Nguyen Q.-L.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 1
71-80
EN
The dynamic evolution with frictional contact of a viscoelastic body is considered. The assumptions on the functions used in modelling the contact are broad enough to include both the normal compliance and the Tresca models. The friction law uses a friction coefficient which is a non-monotone function of the slip. The existence and uniqueness of the solution are proved in the general three-dimensional case.
2
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Analysis and numerical approximation of an elastic frictional contact problem with normal compliance

86%
Han W., Sofonea M.
Applicationes Mathematicae
|
1999
|
tom 26
|
nr 4
415-435
EN
We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show the continuous dependence of the solution on the contact conditions. We also study the finite element approximations of the problem and derive error estimates. Finally, we introduce an iterative method to solve the resulting finite element system.
3
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Quasistatic problems in contact mechanics

86%
Shillor M.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 1
189-204
EN
We describe some of our recent results concerning the modeling and analysis of quasistatic contact problems between a deformable body and a foundation. We concentrate mainly on frictional contact, and in some of the problems thermal effects and the wear of the contacting surfaces are also taken into account. We describe the physical processes involved, the mathematical models, their variational formulation and then present statements of our results. We conclude with a description of some unresolved problems.
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