Numerical Approach of Contact Using an Augmented Lagrangian Method

Abstract

For most engineering applications, contact interactions between deformable bodies are usually modelled by means of given bilateral boundary conditions. Such models are too coarse when the contact region behaviour is subject to interest. In these cases where the boundary is evolving during the loading„ unilateral contact is needed. Finite elements modelling unilateral contact with friction in two-dimensional, axisymmetric and three-dimensional cases have been implemented in the finite element code LAGAMINE developed by the M.S.M. department of University of Liège (Charlier and Habraken 1990, Cescotto and Charlier 1993). They take into account large displacements and rotations between a deformed body and a so-called tool or between two deformed bodies. Until now, we have used a penalty method and a Coulomb dry friction law to describe the interface behaviour. But it is well known that penalty method suffers from ill-conditioning that worsens as penalty values are increased. Constraints are satisfied only in the limit of infinite penalty values. Thus, for many problems it may be desirable or even necessary to consider the augmented Lagrangian technique as an alternative approach capable of circumventing these difficulties.