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An optimization-based algorithm for Coulomb frictional contact

Florent Cadoux 1
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 : The main goal of this paper is to propose a stable algorithm to compute friction forces governed by Coulomb's law in the course of the simulation of a nonsmooth Lagrangian dynamical system. The problem appears in computational mechanics, to simulate the dynamics of granular materials, robots, etc . Using a classical impulse-velocity formulation of Coulomb's law to model friction, and a semi-implicit time discretization scheme, we get a set of linear, non-linear and complementarity equations which has to be solved at each timestep. Two mutually dual parametric convex optimization problems coupled with a fixed point equation appear naturally. By solving (one of) these optimization problems iteratively within a damped nonsmooth-Newton algorithm, it is possible to decrease some infeasibility criterion and hopefully converge to a solution of the system. Numerical results are provided, which show that the number of iterations needed by the algorithm is very small in general and that the method is stable.
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https://hal.inria.fr/inria-00396292
Contributor : Florent Cadoux <>
Submitted on : Wednesday, June 17, 2009 - 2:40:01 PM
Last modification on : Tuesday, February 9, 2021 - 3:20:07 PM

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Florent Cadoux. An optimization-based algorithm for Coulomb frictional contact. CANUM 2008 - 39e Congrès National d'Analyse Numérique, May 2008, Saint Jean de Monts, France. pp.54-69, ⟨10.1051/proc/2009019⟩. ⟨inria-00396292⟩

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