Numerical Solution of Viscoplastic Flow Problems by Augmented Lagrangians

This paper describes an application of augmented Lagrangian techniques to the numerical solution of quasistatic flow problems in incompressible viscoplasticity, focusing on cases where the internal viscoplastic dissipation potential is not a differentiable function of the material deformation rate. The stresses of elastic origin are neglected, and the variational formulation of these problems is approximated via low-order mixed finite elements, which reduces the original problems to the constrained minimization of a convex, but possibly not differentiable functional. Convergence results are proved or recalled, both for the finite element approximation and for the augmented Lagrangian algorithm. A detailed study of the local minimization problems which occur in the augmented Lagrangian decomposition of the above problems is also presented, together with several numerical results.