Nonisothermal Kinematic Hardening Law in Plasticity

The incremental stress-strain relations have been formulated for nonisothermal kinematic hardening materials in which the yield surface is assumed to change its size with temperature. By following Prager's assumption, the yield surface undergoes a translation in the direction of the plastic strain increment during the plastic flow. As pointed out by Shield and Ziegler, the yield surface with Prager's hardening rule, in general, does not satisfy the invariance requirement with respect to a reduction in dimensions in the stress space. Nevertheless, if the von Mises criterion is adopted, such a discrepancy would not arise. If, however, other types of criterion are used, such as Tresca criterion, Ziegler's modification must be incorporated.