$\mathrm{\Delta }$	Generic material plane
$G$	Shear modulus
${\sigma }_i\left(t\right) \left(i=x,y,z\right)$	Normal stress components
${\epsilon }_i\left(t\right)\left(i=x,y,z\right)$	Normal strain components
${\tau }_{ij}\left(t\right) \left(i,j=x,y,z\right)$	Shear stress components
${\gamma }_{ij}\left(t\right) \left(i,j=x,y,z\right)$	Shear strain components
$\mathit{n},\mathit{a},\mathit{b}$	Three axial vector of the second reference coordinate
$\mathit{q}$	Generic direction on candidate material planes
$\theta , \phi ,\alpha$	Euler angles
${\sigma }_n\left(t\right)$	Stress normal to $\mathrm{\Delta }$ plane
${\epsilon }_n\left(t\right)$	Strain normal to $\mathrm{\Delta }$ plane
${\tau }_q\left(t\right)$	Shear stress along the direction $\mathit{q}$
$\mathrm{\Delta }{\gamma }_i$	Shear strain ranges on the ith candidate plane
$p$	Number of subdivisions in one cycle
$\mathrm{\Delta }{\epsilon }_n$	Normal strain ranges acting on the critical plane
${\sigma }_{n,max}$	Maximum normal stress normal to critical plane
${\gamma }_a$	Maximum shear strain amplitude on the critical plane
$S$, $k$	Material constants
$v_e$, $v_p$	Elastic and plastic Poisson’s ratio
$v^{*}$	Effective Poisson’s ratio
${\sigma }_f^{\prime }$	Fatigue strength coefficient
${\epsilon }_f^{\prime }$	Fatigue ductility coefficient
$b$	Fatigue strength exponent
FS	Fatemi-Socie
WB	Wang-Brown
MDP	Maximum damage parameter
E	Young modulus
$N_{fp}$	Model predicted life
$N_f$	Number of cycles to failure
${\sigma }_{n,mean}$	Normal mean stress normal to critical plane
$\mathrm{\Delta }\epsilon$	Axial strain in uniaxial fatigue tests
${\sigma }_{mean}$	Axial mean stress in uniaxial fatigue tests
${\tau }_f^{\prime }$	Shear fatigue strength coefficient
${\gamma }_f^{\prime }$	Shear fatigue ductility coefficient
$b_0$	Shear fatigue strength exponent
$c_0$	Shear fatigue ductility exponent
${\sigma }_y$	Yield strength
${\gamma }_q\left(t\right)$	Shear strain along the direction $\mathit{q}$
$K^{\prime }$	Cyclic strength coefficient
$n^{\prime }$	Cyclic strain hardening exponent
${\sigma }_{a,rs}$	Real normal stress amplitude on plane with shear behavior
${\epsilon }_{a,rs}$	Real normal strain amplitude on plane with shear behavior
${\sigma }_{a,r}$	Real normal stress amplitude on plane without shear behavior
${\epsilon }_{a,r}$	Real normal strain amplitude on plane without shear behavior
${\sigma }_{a,RO}$	Normal stress calculated by Ramberg-Osgood equation
${\sigma }_{a,E}$	Normal stress calculated by Young modulus
$N_{ft}$	Experimental life
$P_{error}$	Model prediction error
$c$	Fatigue ductility exponent
SWT	Smith-Watson-Topper
ECP	Energy-critical plane