whereand
stand
for the shear and bulk moduli, and
is the deviatoric part of the fourth-rank identity tensor,
.
The current UVP model includes both non-linear kinematic hardening
back-stresses,
,
related to the motion of center of yield surface, and isotropic
hardening drag stress,
,
related to the yield surface expansion, after cyclic plastic
deformation. Thus, the inelastic visco-plastic strain-rate flow
rule,,
based on the von-Mises yield function,
,
can be assumed to be independent of hydrostatic pressure and defined
such that: