Symbol	Definition
a	material parameter representing rate sensitivity of slip system
$a_1$ to $a_5$	material parameter for magnetic loss model
A	activation area
$A_{\mathrm{f}}$	material parameter for Freiberg flow stress law
$A_{\theta }$	magnetic A-Parameter
$\alpha$	dislocation to dislocation interaction constant
${\alpha }_j$	angles of the respective layer
$\alpha ,\beta$	slip system or material parameter for magnetic loss model
b	Burgers vector
bcc	body centered cubic
$B_{\max }$	maximal magnetic flux density
$c_1$	grain size effect parameter
$c_2$	dislocation density effect parameter
$c_3$	spontaneous annihilation effect parameter
$c_4$	annihilation by diffusion effect parameter
$c_5$	speed of dislocations effect parameter
$c_6$	mobile dislocations effect parameter
$c_7/c_8$	shearing effect parameters
$c_9$	activation volume effect parameter
CPFEM	crystal plasticity finite-element method
d	grain size
$d_{\mathrm{sheet}}$	sheet thickness
$d_{sp}$	critical distance for spontaneous annihilation
$D_s$	self-diffusion coefficient
$\eta$	scale factor
f	frequency
$f_{\mathrm{n}}$	nucleation frequency
F	deformation gradient
G	shear modulus
$\gamma$	grain boundary energy
${\gamma }_{GB}$	surface energy of the new grain boundary
${\gamma }_n$	surface energy of the nuclei
${\dot{\gamma }}^{\alpha }$	shear rate
${\dot{\gamma }}_{{}_0}$	reference shear rate
h	height of strip
$h_{\mathrm{P}}$	Planck’s quantum of action
$h_{{}_{tot}}$	total height of the strip
$h_1$	smallest roll gap height
H	displacement gradient
$H_{\mathrm{texture}}$	texture related magnetic field strength
HAGB	high-angle grain boundary
i	counting index
j	index indicating individual layer
J	magnetic polarization
k	Boltzmann constant
$\kappa$	yield across grain boundaries
$l_d$	projected arc contact between rolls and metal
$L_p$	plastic velocity gradient
M	Taylor factor
m	unit vector for the slip direction
$m_i$	material parameters for Freiberg flow stress law
${\mu }_{GB}$	high-angle grain boundary mobility
n	normal to the slip plan of slip system $\alpha$
$n_r$	rotational frequency
N	total number of grains
$\dot{N}$	nucleation rate
$N_{\mathrm{ig}}$	number of inner grains
$N_{\mathrm{sg}}$	number of surface grains
ND	normal direction
NO	non-oriented
$\omega$	weighting factor
$\mathsf{\Omega }$	computational domain
ODF	orientation distribution function
$P_{{}_{RX}}$	pressure on an individual grain boundary
$\phi$	logarithmic strain
$\mathsf{\Phi }(t,x)$	level-set function
$\dot{\phi }$	logarithmic rate
${\dot{\phi }}_{{}_{mean}}$	mean logarithmic rate
$q_{{}_{\alpha \beta }}$	measure for latent hardening
$Q_{{}_{diff}}$	self-diffusion activation energy
R	universal gas constant
$R_N$	nucleation radius
$R_r$	roll radius
RD	rolling direction
RVE	representative volume element
$\rho$	density
${\rho }_{{}_{el}}$	electric resistivity
S	interface
SEE	dislocation density
${\sigma }_{\mathrm{f}}$	flow stress
${\sigma }_{\mathrm{f}}\mathrm{mean}$	mean flow stress
${\sigma }_{\mathrm{h}}$	initial hardening stress
${\sigma }_{\mathrm{ig}}$	flow stress of inner grains
${\sigma }_{\mathrm{sg}}$	flow stress of surface grains
${\tau }^{\alpha }$	resolved shear stress of slip system $\alpha$
${\tau }_c^{\alpha }$	critical resolved shear stress of slip system $\alpha$
${\tau }_{\mathrm{s}}$	saturated flow stress
${\tau }_{\mathrm{R}}$	resolved shear stress
TD	transversal direction
$\theta$	misorientation angle or angle relative to rolling direction
$\vartheta$	temperature
$u_a,u_b$	history of the displacement vectors
v	velocity
$v_f$	Debye-frequency
w	slip hardening exponent
wt.%	weight percent
x	position coordinate in the roll gap
$X_a,X_b$	position vectors of the opposite node pairs of the RVE
XRD	X-ray diffraction