We are interested in the finite element approximation of Coulomb's frictional unilateral contact problem in linear elasticity. Using a mixed finite element method and an appropriate regularization, it becomes possible to prove existence and uniqueness when the friction coefficient is less than Cε^{2}|log(h)|^{-1}, where h and ε denote the discretization and regularization parameters, respectively. This bound converging very slowly towards 0 when h decreases (in comparison with the already known results of the non-regularized case) suggests a minor dependence of the mesh size on the uniqueness conditions, at least for practical engineering computations. Then we study the solutions of a simple finite element example in the non-regularized case. It can be shown that one, multiple or an infinity of solutions may occur and that, for a given loading, the number of solutions may eventually decrease when the friction coefficient increases.
@article{bwmeta1.element.bwnjournal-article-amcv12i1p41bwm,
author = {Hild, Patrick},
title = {On finite element uniqueness studies for Coulombs frictional contact model},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {12},
year = {2002},
pages = {41-50},
zbl = {1041.74070},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv12i1p41bwm}
}
Hild, Patrick. On finite element uniqueness studies for Coulombs frictional contact model. International Journal of Applied Mathematics and Computer Science, Tome 12 (2002) pp. 41-50. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv12i1p41bwm/
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