Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 30, Issue 2, Pages 572-596Publisher
SIAM PUBLICATIONS
DOI: 10.1137/060671061
Keywords
3D Coulomb friction; contact problems; dual Lagrange multipliers; inexact primal-dual active set strategy; semismooth Newton methods; nonlinear multigrid method
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In this paper, efficient algorithms for contact problems with Tresca and Coulomb friction in three dimensions are presented and analyzed. The numerical approximation is based on mortar methods for nonconforming meshes with dual Lagrange multipliers. Using a nonsmooth complementarity function for the three-dimensional friction conditions, a primal-dual active set algorithm is derived. The method determines active contact and friction nodes and, at the same time, resolves the additional nonlinearity originating from sliding nodes. No regularization and no penalization are applied, and superlinear convergence can be observed locally. In combination with a multigrid method, it defines a robust and fast strategy for contact problems with Tresca or Coulomb friction. The efficiency and flexibility of the method is illustrated by several numerical examples.
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