research-article

A Uniqueness Criterion for the Signorini Problem with Coulomb Friction

Author:

Yves RenardAuthors Info & Claims

SIAM Journal on Mathematical Analysis, Volume 38, Issue 2

Pages 452 - 467

https://doi.org/10.1137/050635936

Published: 01 January 2006 Publication History

Abstract

The purpose of this paper is to study the solutions to the Signorini problem with Coulomb friction (the so-called Coulomb problem). Some optimal a priori estimates are given, and a uniqueness criterion is exhibited. Recently, nonuniqueness examples have been presented in the continuous framework. It is proved, here, that if a solution satisfies a certain hypothesis on the tangential displacement and if the friction coefficient is small enough, it is the unique solution to the problem. In particular, this result can be useful for the search of multisolutions to the Coulomb problem because it eliminates a lot of uniqueness situations.

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Cited By

Gfrerer HMandlmayr MOutrata JValdman J(2023)On the SCD semismooth* Newton method for generalized equations with application to a class of static contact problems with Coulomb frictionComputational Optimization and Applications10.1007/s10589-022-00429-086:3(1159-1191)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s10589-022-00429-0
Chouly FHild PLleras VRenard Y(2022)Nitsche method for contact with Coulomb frictionJournal of Computational and Applied Mathematics10.1016/j.cam.2022.114557416:COnline publication date: 16-Aug-2022
https://dl.acm.org/doi/10.1016/j.cam.2022.114557
Bretin EChapelat JOuttier PRenard Y(2022)Shape optimization of a linearly elastic rolling structure under unilateral contact using Nitsche’s method and cut finite elementsComputational Mechanics10.1007/s00466-022-02164-z70:1(205-224)Online publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1007/s00466-022-02164-z

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A Uniqueness Criterion for the Signorini Problem with Coulomb Friction

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cover image SIAM Journal on Mathematical Analysis

SIAM Journal on Mathematical Analysis Volume 38, Issue 2

2006

310 pages

ISSN:0036-1410

DOI:10.1137/sjmaah.2006.38.issue-2

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Copyright © 2006 Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 2006

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Cited By

Gfrerer HMandlmayr MOutrata JValdman J(2023)On the SCD semismooth* Newton method for generalized equations with application to a class of static contact problems with Coulomb frictionComputational Optimization and Applications10.1007/s10589-022-00429-086:3(1159-1191)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s10589-022-00429-0
Chouly FHild PLleras VRenard Y(2022)Nitsche method for contact with Coulomb frictionJournal of Computational and Applied Mathematics10.1016/j.cam.2022.114557416:COnline publication date: 16-Aug-2022
https://dl.acm.org/doi/10.1016/j.cam.2022.114557
Bretin EChapelat JOuttier PRenard Y(2022)Shape optimization of a linearly elastic rolling structure under unilateral contact using Nitsche’s method and cut finite elementsComputational Mechanics10.1007/s00466-022-02164-z70:1(205-224)Online publication date: 1-Jul-2022
https://dl.acm.org/doi/10.1007/s00466-022-02164-z

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