Symbol	Abbreviations
$\mathrm{T}$	Temperature
$\dot{\mathsf{\epsilon }}$	Strain rate
$\mathrm{F}$	Deformation gradient
${\mathrm{F}}^{\mathrm{e}}$	Elastic component of deformation gradient
${\mathrm{F}}^{\mathrm{p}}$	Plastic component of deformation gradient
$\mathrm{L}$	Velocity gradient tensor
${\mathrm{L}}^{\mathrm{e}}$	Elastic component of velocity gradient tensor
${\mathrm{L}}^{\mathrm{p}}$	Plastic component of velocity gradient tensor
${\tilde{\mathrm{L}}}^{\mathrm{p}}$	$\mathrm{pull}-\mathrm{back} \mathrm{of} \mathrm{the} \mathrm{plastic} \mathrm{velocity} \mathrm{gradient} \mathrm{to} \tilde{\beta }$
$\tilde{\mathsf{\beta }}$	locally stress-free intermediate configuration
${\dot{\mathsf{\gamma }}}^{\mathrm{a}}$	shearing rate on the α-slip system
$\mathrm{n}$	potential slip system’s number
${\mathrm{S}}^{\mathrm{a}}$	Schmid tensor ${(=m}_0^a ⮾ n_0^a)$, $m_0^{\alpha }$ and $n_0^{\alpha }$ are orthogonal to each other
${\mathrm{m}}_0^{\mathrm{a}}$	Slip plane direction
${\mathrm{n}}_0^{\mathrm{a}}$	Slip plane normal
${\mathrm{m}}^{\mathsf{\alpha }}$	Slipping direction
${\mathrm{n}}^{\mathsf{\alpha }}$	Equivalent slip plane normal
${\mathrm{S}}^{\mathrm{e}}$	The second Paola-Kirchhoff stress tensor
$\mathsf{\sigma }$	Cauchy stress tensor
$\mathrm{E}$	The elastic Green-Lagrange strain tensor
${\mathrm{C}}^{\mathrm{e}}$	The elastic right Cauchy-Green deformation tensor
$\mathrm{I}$	Identity tensor
$\mathsf{\theta }$	The absolute temperature (K)
${\mathsf{\tau }}^{\mathsf{\alpha }}$	The resolved shear stress tensor
$\mathrm{b}$	The magnitude of the Burgers vector
${\mathsf{\rho }}^{\mathsf{\alpha }}$	The mobile dislocations density on the $\alpha$ slip system.
${\overline{\mathrm{v}}}^{\mathsf{\alpha }}$	The average velocity of mobile dislocations on the $\alpha$ slip system.
$\overline{\mathrm{v}}$	The average dislocation velocity
${\mathrm{l}}_{\mathrm{f}}$	The average distance between each obstacle on the slip plane.
${\mathrm{t}}_{\mathrm{w}}$	The waiting time for a dislocation to surpass the local obstacles.
${\mathrm{v}}_{\mathrm{D}}$	The Debye frequency
${\mathrm{k}}_{\mathrm{B}}$	The Boltzmann constant
$∆{\mathrm{G}}^{\ast }$	The difference in the activation-free enthalpy when the dislocation segment moves from the stable configuration to the unstable configuration
${\dot{\mathsf{\gamma }}}_0$	The reference slip rate
$\mathrm{c}$	The fraction of the shearing rate by the total dislocation
$\mathrm{L}$	The mean free path
${\mathrm{y}}_{\mathrm{c}}$	The critical annihilation distance for canceling out the two dislocations with opposite polarities
${\mathsf{\rho }}^{\mathsf{\alpha }}$	The total dislocation density
${\mathsf{\rho }}_{\mathrm{e}}^{\mathsf{\alpha }}$	Edge dislocation component
${\mathsf{\rho }}_{\mathrm{s}}^{\mathsf{\alpha }}$	Screw dislocation component
${\dot{\mathsf{\rho }}}_{\mathrm{i}}^{\mathsf{\alpha }}$	The dislocation density evaluation, where: $i=e,s$
${\widehat{\mathrm{y}}}_{\mathrm{s}}$	The reference critical annihilation distance
$\mathrm{a}$	Constant = 0.001
$\mathrm{b}$	Constant = 8.617E-5
${\mathrm{S}}_{\mathrm{T}}^{\mathsf{\alpha }}$	The total athermal slip resistance parameters
b	The Burgers vector’s magnitude
$\mathsf{\mu }$	The shear modulus,
λ	For identifying the deviations from the regular spatial arrangements of dislocation density
${\mathrm{h}}^{\mathsf{\alpha }\mathsf{\beta }}$	The matrix of dislocation interaction
${\mathsf{\delta }}^{\mathsf{\alpha }\mathsf{\beta }}$	The Kronecker delta
${\mathsf{\omega }}_1$, ${\mathsf{\omega }}_2$	The interaction coefficients
$\mathrm{R}$	correlation coefficient
$\mathrm{A}\mathrm{A}\mathrm{R}\mathrm{E}$	average absolute relative error
$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$	root mean square error
$\mathrm{N}$	The total number of points included in the analysis
${\mathsf{\sigma }}_{\mathrm{E}}^{\mathrm{i}}$	The experimental stress values
${\mathsf{\sigma }}_{\mathrm{P}}^{\mathrm{i}}$	The predicted stress values
${\overline{\mathsf{\sigma }}}_{\mathrm{E}}$	The mean values of experimental stress
${\overline{\mathsf{\sigma }}}_{\mathrm{P}}$	The mean values of predicted stress
${\mathsf{\sigma }}_{\mathrm{a}}$	The athermal activation flow stress
${\mathsf{\sigma }}_{\mathrm{t}\mathrm{h}}$	The thermal activation flow stress.
$\mathrm{B}\mathrm{C}\mathrm{C}$	Body-centered cubic
$\mathrm{F}\mathrm{C}\mathrm{C}$	face-centered cubic
${\mathrm{C}}_0,{\mathrm{C}}_1$, ${\mathrm{C}}_2$, ${\mathrm{C}}_3$, ${\mathrm{C}}_4{,\mathrm{C}}_5$, $\mathrm{n}$	material constants
$\mathrm{T}$	The testing temperature
$\mathsf{\sigma }$	Von-Mises flow stress
$\mathsf{\epsilon }$	equivalent plastic strain
${\dot{\mathsf{\epsilon }}}_{\mathrm{r}}$	reference strain rates
${\mathsf{\epsilon }}^{·\ast }$	the ratio between the testing $\dot{\epsilon }$ and ${\dot{\epsilon }}_r$ (${\epsilon }^{·\ast }={\displaystyle \frac{\dot{\epsilon }}{{\dot{\epsilon }}_r}}$)
${\mathrm{T}}_{\mathrm{r}}$	Reference temperatures
${\mathrm{T}}^{\ast }$	The difference between testing $T$ and $T_r$ ($T^{\ast }=$$T-T_r)$
${\mathrm{m}}_2$, ${\mathrm{m}}_1,{\mathrm{C}}_2,{\mathrm{C}}_1,{\mathrm{B}}_3,{\mathrm{B}}_2,{\mathrm{B}}_1,$$\mathrm{A}$	material constants
${{\mathrm{T}}^{\ast }}_{\mathrm{S}1}$	${T^{\ast }}_{S1}={\displaystyle \frac{T-T_r}{T_m-T_r}}$
${\mathrm{T}}_{\mathrm{m}}$	The melting temperature of AA6082 Al-Mg-Si
${\mathrm{A}}_{\mathrm{i}}$	constants correlate with the ${\epsilon }^i$
${\mathsf{\epsilon }}^{\mathrm{i}}$	representing the strain-hardening component
${\mathrm{C}}_{\mathrm{i}\mathrm{j}}$	constants associate with the ${\epsilon }^{·\ast }$
${\mathrm{m}}_{\mathrm{i}\mathrm{j}\mathrm{k}}$	constants related to the softening parameter $T^{\ast }$