LCF	Low cycle fatigue
2D	Two-dimensional
3D	Three-dimensional
RVE	Representative volume element
S	Deviatoric stress
$\mathsf{\kappa }$	Backstress
${\sigma }_0$	Initial yield stress
R	Isotropic hardening
b	Rate of isotropic hardening
Q	Maximum variation in the size of yield surface
${\epsilon }_{\mathrm{eq}}$	Equivalent plastic strain
${\epsilon }_{\mathrm{a},\mathrm{t}}$	Total-strain amplitude
Ci	Kinematic hardening moduli for J2
$g$ i	Rate of kinematic hardening moduli for J2
N	Number of backstress terms for J2
Ai	Kinematic hardening moduli for CP
Bi	Rate of kinematic hardening moduli for CP
NB	Number of backstress terms for CP
$d{\epsilon }_p$	Plastic strain
CP	Crystal plasticity
${\tau }^{\mathrm{a}}$	Resolved shear stress
CRSS (${\tau }_c^{\mathrm{a}}$)	Critical resolved shear stress
UMAT	User material subroutine
m	Rate sensitivity of the slip
$\dot{{\mathsf{\gamma }}_0}$	Reference shear rate
DP	Dual phase
${\dot{\gamma }}^{\mathrm{a}}$	Shear rate with respect to slip system $\mathrm{a}$
${\mathsf{\chi }}_{bk}^{\mathrm{a}}$	Resolved backstress on the glide system
$A_1$, $A_2$	Material parameters
(${\dot{\tau }}_{c, iso}^{\mathrm{a}}$)	Evolution of CRSS
$h_0$,$n$	Slip hardening parameters
${\tau }_{c,s}$	Saturated CRSS
$M_{\mathsf{\alpha }\mathsf{\beta }}$	Hardening matrix
FEM	Finite element method
C11, C12, C44	Elastic constants
W cyc	Dissipated strain energy
E	Young’s modulus
HV	Vickers’ hardness
CPE4	Four-node plane strain element