In the framework of visco-plastic constitutive theory without yield condition

some assumptions dealing with internal variables

internal stress and different potential hardening of material were used to develop new evolutionary equation of internal variables.Based on the Bodner-Partom model

a two-stage hardening (TSH) model and a multi-stage hardening(MSH) model were established to improve the accuracy of modeling strain rate-dependent tension and cyclic visco-plasticity

especially for ratcheting.The TSH model improves the precision of modeling monotonic tension and cyclic hardening

while the MSH model has more capability of modeling cyclic mean stress relaxation and ratcheting under asymmetric loading condition.