Line-search methods in general return mapping algorithms with application to porous plasticity

The present paper focuses on the application of line-search methods in general return mapping algorithms. Two inexact line-search methods and an exact line-search method are investigated regarding their convergence properties within an automatic time incrementation in finite element calculations. As an example for the assessment of the algorithms, an elastic-plastic and an elastic-viscoplastic version of Gurson's porous plasticity model are used in simulations of the necking of a tensile bar. It is shown that larger time increments are possible and, therefore, a smaller number of increments are required when using line-search methods. The exact line-search method shows the best performance concerning the required number of increments, but takes more CPU time to complete the simulation. The application of the inexact line search methods in general lowers the number of increments along with a reduction in the CPU time, as compared with the case when no line-search is used.