An improved iterative method for large strain viscoplastic problems

In this work, some techniques are proposed to improve the usual Newton{Raphson Method (NRM) used in the numerical analysis of large strain viscoplastic problems. These techniques, based on the rst-order perturbation technique, allow to de ne an adaptive step strategy and to improve the trial solution (guessed solution) for the rst iteration at each step. To assess the e ciency of the proposed techniques, a number of numerical examples are presented: necking of a circular bar, plane strain bending, and an axisymmetric hydrostatic bulging process. Compared with the classical Newton{Raphson method, the proposed scheme requires less matrix inversions, less time steps and less CPU time. For a typical axisymmetric hydrostatic bulging process (606 degrees of freedom), the proposed method needs 5 times less matrix inversions, 1 7 times less time steps, and 4 times less CPU time. Copyright