An adaptive time-stepping scheme for the viscoplasticity theory based on overstress

Abstract

A finite element time-integration method for the viscoplasticity theory based on overstress with variable time steps is developed. The criterion for time-step change is based on the truncation error of multistep methods modified by the magnitude of the deviatoric strain tensor. Time-step changes are affected by an empirical formula which captures the characteristics of the viscoplasticity theory based on overstress. The adaptive scheme is incorporated in the forward gradient (one-step method) and two-step methods developed previously. Results for uniaxial loading and for an internally pressurized cylinder under plane strain indicate that the respective adaptive methods are more accurate and more economical than the forward gradient and the two-step methods.