The present work provides a profound analytical and numerical analysis of the
material properties of SFRC on the mesoscale as well as the resulting
correlation structure taking into account the probabilistic characteristics of
the fiber geometry. This is done by calculating the engineering constants using
the analytical framework given by Tandon and Weng as well as Halpin and Tsai.
The input parameters like fiber length, diameter and orientation are chosen
with respect to their probability density function. It is shown, that they are
significantly influenced by the fiber length, the fiber orientation and the
fiber volume fraction. The verification of the analytically obtained values is
done on a numerical basis. Therefore, a two-dimensional microstructure is
generated and transferred to a numerical model. The advantage of this procedure
is, that there are several fibers with different geometrical properties placed
in a preset area. The results of the numerical analysis meet the analytically
obtained conclusions. Furthermore, the results of the numerical simulations are
independent of the assumption of a plane strain and plane stress state,
respectively. Finally, the correlation structure of the elasticity tensor is
investigated. Not only the symmetry properties of the elasticity tensor
characterize the correlation structure, but also the overall
transversely-isotropic material behavior is confirmed. In contrast to the
influencing parameters, the correlation functions vary for a plane strain and a
plane stress state.