A universal integration algorithm for rate-dependent elastoplasticity

An algorithm is developed for integrating rate-dependent constitutive equations of elstoplasticity including isotropic and kinematic hardening, as well as thermal softening and non-coaxiality of the plastic strain rate and the driving stress. The method is unconditionally stable and accurate for large time steps and all possible ranges of rate-dependency. Under a constant loading rate the algorithm gives exact results at arbitrary step sizes for rate-independent materials without hardening, and in proportional loading for rate-independency with hardening, and linear viscosity without hardening. The present method is an extension of a recently proposed integration algorithm for stiff equations to domains of high rate-sensitivity like, for example, in power-law creep. The algorithm employs a plastic predictor-elastic corrector scheme, which, in general, requires less numerical effort in the return mapping process than the assumption of an elastic predictor. Numerical examples underline the efficiency of this integration algorithm in comparison to gradient techniques and an extended radial return method for rate-dependent plasticity.