Augmented Lagrangian procedure for implicit computation of contact-impact between deformable bodies

Denis Graillet (1) , Jean-Philippe Ponthot (1) , Laurent Stainier (1)

1 LTAS - Aerospace and Mechanical Engineering Department [Liège]

This paper shows how efficiency can be improved by using an adequate Augmented Lagrangian procedure instead of the classical and well-known Penalty method for solving contact-impact problems between deformable bodies, including frictional contact, large deformations, dynamical effects and inelasticity phenomena. The Augmented Lagrangian method has already enjoyed great success in solving constrained minimisation problems or incompressibility conditions. Alternatives to existing automation techniques for augmentations are presented. Starting from a Penalty method, it will be seen how the Augmented Lagrangian decreases ill-conditioning of governing equations and gives a more precise solution with a lower CPU-cost. Several original simultaneous criteria are proposed for optimising the number and the location of the augmentations in an incremental implicit resolution. Application of the method is done for two axisymmetric impact problems.

Domaines: Mécanique [physics.med-ph]; Matériaux

Denis Graillet, Jean-Philippe Ponthot, Laurent Stainier. Augmented Lagrangian procedure for implicit computation of contact-impact between deformable bodies. International Journal of Crashworthiness, 2001, 6 (2), pp.209-222. ⟨10.1533/cras.2001.0173⟩. ⟨hal-01005280⟩