We consider quasistatic evolution of a viscoelastic body which is in bilateral frictional contact with a rigid foundation, We derive two variational formulations for the problem: the primal formulation in terms of the displacements and the dual formulation in terms of the stress field. We prove the existence of a unique solution to each one and establish the equivalence between the two variational formulations. We also prove the continuous dependence of the solution on the friction yield limit.
Publié le : 2001-11-04
Classification:
Quasistatic bilateral frictional contact,
Viscoelastic constitutive law,
Dual problem,
Fixed point,
Tresca's law of friction,
[MATH]Mathematics [math]
@article{hal-01352587,
author = {Awbl, B. and Shillor, M. and Sofonea, M.},
title = {Dual formulation of a quasistatic viscoelastic contact problem with tresca's friction law},
journal = {HAL},
volume = {2001},
number = {0},
year = {2001},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01352587}
}
Awbl, B.; Shillor, M.; Sofonea, M. Dual formulation of a quasistatic viscoelastic contact problem with tresca's friction law. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-01352587/