  One of the essential questions in the area of granular matter is, how to
obtain macroscopic tensorial quantities like stress and strain from
``microscopic'' quantities like the contact forces in a granular assembly.
Different averaging strategies are introduced, tested, and used to obtain
volume fractions, coordination numbers, and fabric properties. We derive anew
the non-trivial relation for the stress tensor that allows a straightforward
calculation of the mean stress from discrete element simulations and comment on
the applicability. Furthermore, we derive the ``elastic'' (reversible) mean
displacement gradient, based on a best-fit hypothesis. Finally, different
combinations of the tensorial quantities are used to compute some material
properties.
  The bulk modulus, i.e. the stiffness of the granulate, is a linear function
of the trace of the fabric tensor which itself is proportional to the density
and the coordination number. The fabric, the stress and the strain tensors are
{\em not} co-linear so that a more refined analysis than a classical elasticity
theory is required.
