[Influence des paramètres d’algorithmes de résolution de contact frottant sur la solution obtenue à convergence : étude sur un problème avec frottement de Coulomb à solutions multiples]
In this paper, we compare four algorithms solving the quasi-static contact between one elastic body and one rigid obstacle in two dimensions. With the Coulomb’s law of friction, this example exhibits multiple solutions if the friction coefficient is larger than 3. After describing the numerical methods tested in this paper, we study the influence of the parameters of the algorithms on the nature of the obtained solution at convergence. On this academic example, we also compute two existing criteria on the uniqueness of the solution. Finally, for friction coefficient larger than 3, we compute a new sliding solution and observe that not all approaches are able to find it.
Ce papier compare quatre méthodes de résolution du problème bi-dimensionnel de contact quasi-statique entre un solide élastique et un obstacle rigide. Sur l’exemple étudié, avec une loi de frottement de Coulomb, plusieurs solutions existent lorsque le coefficient de frottement est plus grand que 3. Après avoir décrit les quatre méthodes numériques comparées, nous les mettons en œuvre sur l’exemple et étudions l’influence des paramètres de ces algorithmes sur la solution obtenue à convergence. Sur cet exemple académique, nous calculons aussi deux critères d’existence de solutions multiples. Enfin, pour un coefficient de frottement strictement supérieur à 3, nous calculons une troisième solution de type glissement et observons que toutes les approches numériques étudiées ne sont pas capables de la trouver.
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Mots-clés : Contact frottant quasi-statique, frottement de Coulomb, algorithmes
Valentine Rey 1
CC-BY 4.0
Valentine Rey. On the influence of resolution algorithm’s parameters on the converged solution for a Coulomb friction contact problem exhibiting multiple solutions. Comptes Rendus. Mécanique, Volume 354 (2026), pp. 461-480. doi: 10.5802/crmeca.362
@article{CRMECA_2026__354_G1_461_0,
author = {Valentine Rey},
title = {On the influence of resolution algorithm{\textquoteright}s parameters on the converged solution for a {Coulomb} friction contact problem exhibiting multiple solutions},
journal = {Comptes Rendus. M\'ecanique},
pages = {461--480},
year = {2026},
publisher = {Acad\'emie des sciences, Paris},
volume = {354},
doi = {10.5802/crmeca.362},
language = {en},
}
TY - JOUR AU - Valentine Rey TI - On the influence of resolution algorithm’s parameters on the converged solution for a Coulomb friction contact problem exhibiting multiple solutions JO - Comptes Rendus. Mécanique PY - 2026 SP - 461 EP - 480 VL - 354 PB - Académie des sciences, Paris DO - 10.5802/crmeca.362 LA - en ID - CRMECA_2026__354_G1_461_0 ER -
%0 Journal Article %A Valentine Rey %T On the influence of resolution algorithm’s parameters on the converged solution for a Coulomb friction contact problem exhibiting multiple solutions %J Comptes Rendus. Mécanique %D 2026 %P 461-480 %V 354 %I Académie des sciences, Paris %R 10.5802/crmeca.362 %G en %F CRMECA_2026__354_G1_461_0
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