Numerical Analysis of Augmented Lagrangian Algorithms in Complementary Elastoplasticity

The main subject of the paper is the investigation of Augmented Lagrangian algorithms and update formulas in the solution of elastoplastic problems. A stress rate formulation for elastoplastic models with internal variables and its finite increment form is employed to state the mechanical problem. In this formulation the Augmented Lagrangian is used to enforce the constraint of plastic admissibility directly on the stresses and thermodynamic forces. This is not a limitation of the Augmented Lagrangian approach, and the same framework can be built on more classical displacement formulations as well. The meaning and the derivation of various first and second order Lagrangian multipliers update formulas and iterative schemes is shown. A new diagonal iteration algorithm and the introduction of a scale factor for the Augmented Lagrangian term are proposed. Numerical examples compare the efficiency of several forms of Augmented Lagrangian algorithms and illustrate the influence of the scale factor and of the penalty parameter.