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Applications of an existence result for the Coulomb friction problem

Vincent Acary 1, * Florent Cadoux 1, * 
* Corresponding author
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
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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Vincent Acary, Florent Cadoux. Applications of an existence result for the Coulomb friction problem. Stavroulakis, Georgios E. Recent Advances in Contact Mechanics, 56, Springer, pp.45-66, 2013, Lecture Notes in Applied and Computational Mechanics, ⟨10.1007/978-3-642-33968-4_4⟩. ⟨hal-00782128⟩



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