Automatic correction of the time step in implicit simulations of the stamping process

A specific aspect of simulations of stamping processes is the numerical method adopted to include the non-linearities associated with the frictional contact problem in large deformation plasticity. In fact, convergence problems are frequently encountered, especially when using a quasi-static implicit algorithm. One way of increasing the numerical robustness of these algorithms is to adopt an augmented Lagrangian method to incorporate the problem of contact with friction. The resulting non-linear system can be solved by a Newton–Raphson type method, for which a trial solution must be given to start the iterative equilibrium loop. The quality of this trial solution is determinant for the convergence of the iterative process. An automatic control of the size of the time step can improve this trial solution. In this study, a new size control for the time step, imposing restrictions not only on the increments of the state variables but also on the increments of the contact forces, is proposed. An example of a bending test is used to analyse the influence of this new limitation on the overall convergence behaviour of the fully implicit code DD3IMP.