  The use of discrete material representation in numerical models is
advantageous due to the straightforward way it takes into account material
heterogeneity and randomness, and the discrete and orientated nature of cracks.
Unfortunately, it also restricts the macroscopic Poisson's ratio and therefore
narrows its applicability. The paper studies the Poisson's ratio of a discrete
model analytically. It derives theoretical limits for cases where the geometry
of the model is completely arbitrary, but isotropic in the statistical sense.
It is shown that the widest limits are obtained for models where normal
directions of contacts between discrete units are parallel with the vectors
connecting these units. Any deviation from parallelism causes the limits to
shrink. A comparison of the derived equations to the results of the actual
numerical model is presented. It shows relatively large deviations from the
theory because the fundamental assumptions behind the theoretical derivations
are largely violated in systems with complex geometry. The real shrinking of
the Poisson's ratio limit is less severe compared to that which is
theoretically derived.
