GTN Model	Gurson–Tvergaard–Needleman Model
VUMAT	User Material Subroutine for Abaqus
Gurson Model	Gurson damage model
ϕ	Yield function
$q$ $,{\sigma }_{eq}$	Von Mises stress
${\sigma }_m$	Yield stress
σℎ	Hydrostatic stress
q1,q2,q3	Empirical parameters in the GTN model
$tr\left(\sigma \right)$	Trace of stress tensor
${\sigma }_{xx},{\sigma }_{yy},{\sigma }_{zz}$	Corresponding to normal stress in x, y and z directions
$f$	Porosity
$f^{\ast }$	$\mathrm{Current}\mathrm{porosity},\mathrm{a}\mathrm{function}\mathrm{of}\mathrm{porosity}f$
$f_c$	Critical pore volume fraction
$f_u^{\ast }$	Porosity value when stress is zero
$f_f$	Pore volume fraction at fracture
$df$	Increment of void fraction
$d{f}_{grow}$	Increment of original void growth
$d{f}_{nucl}$	Increment of new void nucleation
$I$	Second-order unit tensor
$f_n$	Volume fraction of the second phase
${\epsilon }_p$	Macroscopic equivalent plastic strain
${\epsilon }_N$	Average plastic strain of nucleation
$s_N$	Standard deviation, dispersion of nucleation strain
$w\left({\sigma }_{ij}\right)$	Stress state function
$J_3$	The third invariant of the deviatoric stress tensor