On the numerical algorithm for isotropic–kinematic hardening with the Armstrong–Frederick evolution of the back stress Original Research Article

The algorithmic consistency conditions are derived which yield the plastic loading index for the combined isotropic–kinematic hardening plasticity with the Armstrong–Frederick evolution equation for the back stress. Rate-independent elastic–plastic, and rate-dependent viscoelastic–plastic and elastic–viscoplastic material models are all encompassed by the analysis. The directions of the plastic and viscoplastic increments of strain are determined from a developed numerical algorithm, in conjunction with the radial return method. Numerical evaluations are presented to compare the predictions of various models under cyclic loading in simple shear. The effects of different material parameters on stress response are discussed.