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: