Stress-Based Methods for Quasi-Variational Inequalities Associated with Frictional Contact

Bernhard Kober; Gerhard Starke; Rolf Krause; Gabriele Rovi

doi:10.1007/978-3-030-79393-7_18

Stress-Based Methods for Quasi-Variational Inequalities Associated with Frictional Contact

Bernhard Kober, Gerhard Starke^*, Rolf Krause, Gabriele Rovi

^*Corresponding author for this work

Applied Mathematics and Computational Science

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

The stress-based formulation of elastic contact with Coulomb friction in the form of a quasi-variational inequality is investigated. Weakly symmetric stress approximations are constructed using a finite element combination on the basis of Raviart–Thomas spaces of next-to-lowest order. An error estimator is derived based on a displacement reconstruction and proved to be reliable under certain assumptions on the solution formulated in terms of a norm equivalence in the trace space H^1∕2(Γ). Numerical results illustrate the effectiveness of the adaptive refinement strategy for a Hertzian frictional contact problem in the compressible as well as in the incompressible case.

Original language	English (US)
Title of host publication	International Series of Numerical Mathematics
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	445-466
Number of pages	22
DOIs	https://doi.org/10.1007/978-3-030-79393-7_18
State	Published - 2022

Publication series

Name	International Series of Numerical Mathematics
Volume	172
ISSN (Print)	0373-3149
ISSN (Electronic)	2296-6072

Bibliographical note

Publisher Copyright:
© 2022, Springer Nature Switzerland AG.

Keywords

A posteriori error estimation
Coulomb friction
Quasi-variational inequality

ASJC Scopus subject areas

Numerical Analysis
Control and Optimization
Applied Mathematics

Access to Document

10.1007/978-3-030-79393-7_18

Cite this

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title = "Stress-Based Methods for Quasi-Variational Inequalities Associated with Frictional Contact",

abstract = "The stress-based formulation of elastic contact with Coulomb friction in the form of a quasi-variational inequality is investigated. Weakly symmetric stress approximations are constructed using a finite element combination on the basis of Raviart–Thomas spaces of next-to-lowest order. An error estimator is derived based on a displacement reconstruction and proved to be reliable under certain assumptions on the solution formulated in terms of a norm equivalence in the trace space H1∕2(Γ). Numerical results illustrate the effectiveness of the adaptive refinement strategy for a Hertzian frictional contact problem in the compressible as well as in the incompressible case.",

keywords = "A posteriori error estimation, Coulomb friction, Quasi-variational inequality",

author = "Bernhard Kober and Gerhard Starke and Rolf Krause and Gabriele Rovi",

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year = "2022",

doi = "10.1007/978-3-030-79393-7_18",

language = "English (US)",

series = "International Series of Numerical Mathematics",

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Stress-Based Methods for Quasi-Variational Inequalities Associated with Frictional Contact. / Kober, Bernhard; Starke, Gerhard; Krause, Rolf et al.
International Series of Numerical Mathematics. Springer Science and Business Media Deutschland GmbH, 2022. p. 445-466 (International Series of Numerical Mathematics; Vol. 172).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Stress-Based Methods for Quasi-Variational Inequalities Associated with Frictional Contact

AU - Kober, Bernhard

AU - Starke, Gerhard

AU - Krause, Rolf

AU - Rovi, Gabriele

PY - 2022

Y1 - 2022

N2 - The stress-based formulation of elastic contact with Coulomb friction in the form of a quasi-variational inequality is investigated. Weakly symmetric stress approximations are constructed using a finite element combination on the basis of Raviart–Thomas spaces of next-to-lowest order. An error estimator is derived based on a displacement reconstruction and proved to be reliable under certain assumptions on the solution formulated in terms of a norm equivalence in the trace space H1∕2(Γ). Numerical results illustrate the effectiveness of the adaptive refinement strategy for a Hertzian frictional contact problem in the compressible as well as in the incompressible case.

AB - The stress-based formulation of elastic contact with Coulomb friction in the form of a quasi-variational inequality is investigated. Weakly symmetric stress approximations are constructed using a finite element combination on the basis of Raviart–Thomas spaces of next-to-lowest order. An error estimator is derived based on a displacement reconstruction and proved to be reliable under certain assumptions on the solution formulated in terms of a norm equivalence in the trace space H1∕2(Γ). Numerical results illustrate the effectiveness of the adaptive refinement strategy for a Hertzian frictional contact problem in the compressible as well as in the incompressible case.

KW - A posteriori error estimation

KW - Coulomb friction

KW - Quasi-variational inequality

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SP - 445

EP - 466

BT - International Series of Numerical Mathematics

PB - Springer Science and Business Media Deutschland GmbH

ER -

Stress-Based Methods for Quasi-Variational Inequalities Associated with Frictional Contact

Abstract

Publication series

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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