where is the deviatoric stress of Cauthy stress tensor. is the deviatoric part of the back-stress, , which can be further decomposed into two components,
and , to account for the Bauschinger effect56, whilerepresents the initial kinematic hardening produced after the elastic portion, andaccounts for the kinematic hardening due to the later stage of strain hardening. An Armstrong-Frederick56 form has been used to describe the non-linear evolution of the kinematic hardening, including linear hardening term,, and dynamic recovery term, . The Chaboche kinematic hardening decomposition of the elementary back-stress is formulated, as follows: