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Applications of an Existence Result for the Coulomb Friction Problem

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Book cover Recent Advances in Contact Mechanics

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 56))

Abstract

In a recent paper [2], we prove an abstract existence result for the Coulomb friction problem in discrete time. This problem must be solved at each time step when performing a simulation of the dynamics of a mechanical system involving unilateral contact and Coulomb friction (expressed here at the level of velocities). In this paper, we only recall this result and the gist of its proof and then give an overview of its range of applicability to show the power of our existence criterion. By considering several mechanical systems (Painlevé’s example, granular material on a plan or in a drum) and several particular cases (cases with no moving external objects, cases without friction), we demonstrate the broad range of use-cases to which the criterion can be applied by pure abstract reasoning, without any computations. We also show counter-examples where the criterion does not apply. We then turn to more complicated situations where the existence result cannot be used trivially, and discuss the computational methods that are available to check the criterion in practice using optimization software. It turns out that in suffices to solve a linear program (LP) when the problem is bi-dimensional, and a second order cone program (SOCP) when the problem is tri-dimensional.

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Authors and Affiliations

  1. INRIA Rhone-Alpes, Grenoble, France

    Vincent Acary & Florent Cadoux

Authors
  1. Vincent Acary
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  2. Florent Cadoux
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Correspondence to Vincent Acary .

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Editors and Affiliations

  1. Dept. Production Engineering &, Management, Technical University of Crete, Crete, 731 00, Greece

    Georgios E. Stavroulakis

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Acary, V., Cadoux, F. (2013). Applications of an Existence Result for the Coulomb Friction Problem. In: Stavroulakis, G. (eds) Recent Advances in Contact Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33968-4_4

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  • DOI: https://doi.org/10.1007/978-3-642-33968-4_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33967-7

  • Online ISBN: 978-3-642-33968-4

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