In this article, various numerical methods to solve multicontact problems within the nonsmooth discrete element method are presented. The techniques considered to solve the frictional unilateral conditions are based both on the bipotential theory introduced by G. de Saxcé and the augmented Lagrangian theory introduced by P. Alart. Following the ideas of Z.-Q. Feng a new Newton method is developed to improve these classical algorithms, and numerical experiments are presented to show that these methods are faster than the previous ones, provide results with a better quality, and are less sensitive to the numerical parameters. Moreover, a stopping criterion that ensures a good mechanical property of the solution is provided. Copyright © 2012 John Wiley & Sons, Ltd.
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