Algorithms for the analysis of 3D finite strain contact problems

Abstract

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 (C) 2004 John Wiley Sons, Ltd.