  Due to their good ratio of stiffness and strength to weight, foam materials
find use in lightweight engineering. Though, in many applications like
structural bending or tension, the scale separation between macroscopic
structure and the foam's mesostructure like cells size, is relatively weak and
the mechanical properties of the foam appear to be size dependent. Positive as
well as negative size effects have been observed for certain basic tests of
foams, i.e., the material appears either to be more compliant or stiffer than
would be expected from larger specimens. Performing tests with sufficiently
small specimens is challenging as any disturbances from damage of cell walls
during sample preparation or from loading devices must be avoided.
Correspondingly, the number of respective data in literature is relatively low
and the results are partly contradictory.
  In order to avoid the problems from sample preparation or bearings, the
present study employs virtual tests with CT data of real medium-density ceramic
foams. A number of samples of different size is "cut" from the resulting voxel
data. Subsequently, the apparent elastic properties of each virtual sample are
"measured" directly by a free vibrational analysis using finite cell method,
thereby avoiding any disturbances from load application or bearings. The
results exhibit a large scatter of the apparent moduli per sample size, but
with a clear negative size effect in all investigated basic modes of
deformation (bending, torsion, uniaxial). Finally, the results are compared
qualitatively and quantitatively to available experimental data from
literature, yielding common trends as well as open questions.
