A primal-dual active set algorithm for three-dimensional contact problems with Coulomb friction. (English) Zbl 1158.74045

Hüeber, S.; Stadler, G.; Wohlmuth, B. I.

SIAM J. Sci. Comput. 30, No. 2, 572-596 (2008).

Summary: 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 three-dimensional friction conditions, we derive active set algorithm. 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.

MSC:

74S05	Finite element methods applied to problems in solid mechanics
74M15	Contact in solid mechanics
74M10	Friction in solid mechanics

Keywords:

dual Lagrange multipliers; nonlinear multigrid method; mortar methods

Software:

UG