Algorithms for the analysis of 3D finite strain contact problems

From the constraint imposition aspects in 3D to friction regularization, various ideas are exposed in this paper. A variation of the Rockafellar Lagrangian is proposed which results in continuous second‐order derivatives if Lagrange multiplier estimates are greater or equal than one. This fact allows the adoption of a full second‐order (i.e. Lagrange–Newton) method avoiding sequential unconstrained minimization techniques. An algorithm for global and local contact detection is presented which is developed for dealing with large step sizes typical of implicit methods. A modified constraint definition to deal with non‐smooth situations is presented. Aspects of friction implementation, including a regularization scheme which ensures stepwise objectivity, are detailed. Finally, several illustrative examples are carried out with success. Copyright © 2004 John Wiley & Sons, Ltd.