Numerical Integrators for Elastic-Secondary Creep

A method has been developed for building error maps to present the accuracy of time-dependent inelastic material models similar to the error maps used for time-independent plasticity. The elastic-secondary creep constitutive model with a Norton creep behavior is used throughout the paper to illustrate the method. It is noted that this is very simple unified creep-plasticity model with no internal state variables, i.e., no back stress or change in the drag stress. The error maps for nine integrators, which are used or have been proposed to be used for creep or unified creep-plasticity models, are then presented. Included are an explicit Euler integrator, explicit Runge-Kutta methods of second, third, and fourth orders, three implicit integrators, and two integrators, which have been specially designed for this equation. A quantitative measure of the accuracy of an integrator is also defined and applied to the nine integrators. A special integrator for the equation was found to be best and the Euler method ranked sixth. Other considerations for choosing an optimum integrator is also discussed.