Rigid-plastic implicit integration scheme for analysis of metal forming

This paper is devoted to the analysis of metal forming with the assumption of rigid-plastic behavior with strain hardening. As opposed to the classical rate problem formulation based on Markov's principle and the explicit scheme, a more satisfactory incremental implicit approach is deduced from Moreau's catching up algorithm. This implicit scheme, although more complicated, gives better results concerning convergence and numerical stability. Using an internal variable to represent the strain hardening, an incremental strain energy density is defined which leads to the principle of the minimum total incremental strain energy. The frictional contact between the workpiece and the tool is treated by an augmented Lagrangian method. The upsetting problem is simulated and shows that the implicit scheme is faster than the explicit one.