Geodesic
An optimization-based algorithm for Coulomb's frictional contact
Florent Cadoux1
1 Inria, 655 av. de l'Europe, 38334 Montbonnot
ESAIM. Proceedings, Tome 27 (2009), pp. 54-69 Cet article a éte moissonné depuis la source EDP Sciences

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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.
DOI : 10.1051/proc/2009019

Florent Cadoux 1

1 Inria, 655 av. de l'Europe, 38334 Montbonnot 
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     author = {Florent Cadoux},
     title = {An optimization-based algorithm for {Coulomb's} frictional contact},
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     year = {2009},
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     doi = {10.1051/proc/2009019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/2009019/}
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Florent Cadoux. An optimization-based algorithm for Coulomb's frictional contact. ESAIM. Proceedings, Tome 27 (2009), pp. 54-69. doi: 10.1051/proc/2009019

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