The sphere under internal pressure—A comparison of two time-integration schemes for the viscoplasticity theory based on overstress

Numerical inelastic analyses of a hollow sphere under linearly increasing internal pressure are performed using the viscoplasticity theory based on overstress with material constants representing the behavior of AISI Type 304 Stainless Steel at room temperature. The purpose of the investigation was to compare the results of two numerical schemes. The first was a finite element time integration method developed previously and the second was a finite difference scheme which used the IMSL subroutine DGEAR for the time integration. The results show that the finite element solution matches the finite difference results at a fraction of the cost of the finite difference calculation. A comparison is made between the elastic perfectly-plastic and the viscoplastic solutions for the displacement and the stresses.