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2018 | OriginalPaper | Chapter

On Solving Contact Problems with Coulomb Friction: Formulations and Numerical Comparisons

Authors : Vincent Acary, Maurice Brémond, Olivier Huber

Published in: Advanced Topics in Nonsmooth Dynamics

Publisher: Springer International Publishing

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Abstract

In this chapter, we review several formulations of the discrete frictional contact problem that arises in space and time discretized mechanical systems with unilateral contact and three-dimensional Coulomb’s friction. Most of these formulations are well–known concepts in the optimization community, or more generally, in the mathematical programming community. To cite a few, the discrete frictional contact problem can be formulated as variational inequalities, generalized or semi–smooth equations, second–order cone complementarity problems, or optimization problems, such as quadratic programming problems over second-order cones. Thanks to these multiple formulations, various numerical methods emerge naturally for solving the problem. We review the main numerical techniques that are well-known in the literature, and we also propose new applications of methods such as the fixed point and extra-gradient methods with self-adaptive step rules for variational inequalities or the proximal point algorithm for generalized equations. All these numerical techniques are compared over a large set of test examples using performance profiles. One of the main conclusions is that there is no universal solver. Nevertheless, we are able to give some hints for choosing a solver with respect to the main characteristics of the set of tests.

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Available only for authorised users

https://frictionalcontactlibrary.github.io/index.html, which aims to provide many problems to compare algorithms on a fair basis.

http://siconos.gforge.inria.fr.

More information can be found at https://frictionalcontactlibrary.github.io.

The whole collection of problems can be found at https://github.com/FrictionalContactLibrary/fclib-library.

https://git-xen.lmgc.univ-montp2.fr/lmgc90/lmgc90_user/wikis/home.

More information on the software is available at http://siconos.gforge.inria.fr and the software can be downloaded at https://github.com/siconos/siconos.

http://people.sc.fsu.edu/~jburkardt/c_src/csparse/csparse.html.

https://ciment-grid.ujf-grenoble.fr/.

Nevertheless, the reader can have access to the complete list of performance profiles at https://github.com/siconos/faf/blob/master/TeX/Full-test/full-test_current.pdf.

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Title: On Solving Contact Problems with Coulomb Friction: Formulations and Numerical Comparisons
Authors: Vincent Acary
Maurice Brémond
Olivier Huber
Publisher: Springer International Publishing
Book: Advanced Topics in Nonsmooth Dynamics
Print ISBN: 978-3-319-75971-5

Electronic ISBN: 978-3-319-75972-2

Copyright Year: 2018
DOI: https://doi.org/10.1007/978-3-319-75972-2_10

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