the right-handed triad of unit lattice vectors of the active slip system by $\mathbf{s}$, $\mathbf{p}$, and $\mathbf{m}$, where $\mathbf{s}$ points to the slip direction, $\mathbf{p}$ lies in the slip plane and is perpendicular to $\mathbf{s}$, and $\mathbf{m}$ is normal to the slip plane. Without restricting generality we may choose the rectangular cartesian coordinate system $(x_1,x_2,x_3)$ in the reference configuration such that its basis vectors coincide with these lattice vectors (see Fig. \[fig:loop\]) $$\mathbf{e}_1=\mathbf{s},\quad \mathbf{e}_2=\mathbf{p}, \quad \mathbf{e}_3=\mathbf{m}.$$ The plastic deformation is then given by $$\label{eq:2.0}
\mathbf{F}^p=\mathbf{I}+\beta (\mathbf{x})\mathbf{s}\otimes \mathbf{m}=\mathbf{I}+\beta (\mathbf{x})\mathbf{e}_1\otimes \mathbf{e}_3,$$ with $\beta $ being the plastic slip. We assume that all dislocations causing this plastic deformation lie completely in the slip planes and the dislocation network is regular in the sense that nearby dislocations have nearly the same direction and orientation. This enables one to introduce a scalar function $l(x_1,x_2,x_3)$ (called a loop function) such that its level curves $$\label{eq:2.a}
l(x_1,x_2,c_3)=c,$$ with $c_3$ and $c$ being constants, coincide with the dislocation lines. Thus, in this three-dimensional kinematics we admit, according to equation , only the conservative motion of dislocations and exclude from consideration the dislocation climb which is an important mechanism of temperature-dependent creep. We denote by ${\boldsymbol{\nu}}$ and ${\boldsymbol{\tau}}$ the 