Abstract :
A class of generalized mid-point algorithms for pressure-dependent elastoplastic models is formulated in the paper. The accuracies of the formulated generalized mid-point algorithms including the Euler backward algorithm and the one-step Euler forward algorithm are systematically analyzed against the exact solution for Gurson-based pressure-dependent elastoplastic model. The accuracies of the algorithms are assessed by means of iso-error maps. Results show that the formulated generalized mid-point algorithms are reasonably accurate in both small and large increment steps. It is found that in all the cases considered, the maximum errors in the presence of volumetric strain increments are less than those without volumetric strain increments. When the deviatoric strain increments are given in the radial direction, the true mid-point algorithm is the most accurate one. Furthermore, the optimal value α of the generalized mid-point algorithms, in terms of maximum errors, is observed between 0.5 and 1. For both small and large increment steps, the one-step Euler forward algorithm gives the worst accuracy.
