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A generalized Newton method for contact problems with friction

Abstract : This article reviews the numerical methods used for a few years in the program TACT to solve contact problems with non-asseciated Coulomb's friction. These methods include: a penalty method to enforce the contact and adherence conditions respectively, an implicit projection method to integrate the slip rule, the finite element method for the spatial discretization and a generalized Newton method to overcome the contact and friction non linearities. Recent advances improving the robustness of the resulting frictional contact algorithm are reported. In particular, a necessary and sufficient condition on the friction coefficient for the solution to flat contacts to be unique is stated and a damping factor is introduced to guarantee the algorithm convergence to this solution in the two-dimensional case. The flat punch problem is used to illustrate both the accuracy and efficiency of the method.
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Contributor : Mathias Legrand <>
Submitted on : Friday, January 13, 2017 - 1:50:06 AM
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  • HAL Id : hal-01433772, version 1


Alain Curnier, Pierre Alart. A generalized Newton method for contact problems with friction. Journal de Mécanique Théorique et Appliquée, Gauthier-Villars, 1988. ⟨hal-01433772⟩



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