  In this paper three different approaches towards a continuum theory of fiber
suspensions are discussed. The first one is the classical Thermodynamics of
Irreversible Processes with internal variables. It derives constitutive
equations for fiber suspensions on the basis of ONSAGERs phenomenological
coefficients, which are related to the mechanical properties of the fibers.
Secondly another method of exploiting the dissipation inequality, the method
introduced by LIU is applied in order to derive results on constitutive
equations. Finally a mesoscopic background theory is discussed. In this
approach a distribution of different fiber orientations and fiber deformations
is assumed. The fiber orientation and deformation are additional variables in
the domain of field quantities. The new field quantities on the enlarged set of
variables obey balance equations. The mesoscopic balance of mass results in an
equation of motion for the distribution of fiber orientations and deformations.
The usual macroscopic fields of continuum mechanics are averages of mesoscopic
fields over the different orientations and deformations. Macroscopic quantities
characterizing the orientational order, the alignment tensors are defined by
the help of the orientation distribution function. They are internal variables
in the macroscopic theory characterizing the distribution of fiber
orientations.
