  In this work the linear elastic properties of materials containing spherical
voids are calculated and compared using finite element simulations. The focus
is on homogeneous solid materials with spherical, empty voids of equal size.
The voids are arranged on crystalline lattices (SC, BCC, FCC and HCP structure)
or randomly, and may overlap in order to produce connected voids. In that way,
the entire range of void fraction between 0.00 and 0.95 is covered, including
closed-cell and open-cell structures. For each arrangement of voids and for
different void fractions the full stiffness tensor is computed. From this, the
Young's modulus and Poisson ratios are derived for different orientations.
Special care is taken of assessing and reducing the numerical uncertainty of
the method. In that way, a reliable quantitative comparison of different void
structures is carried out. Among other things, this work shows that the Young's
modulus of FCC in the (1 1 1) plane differs from HCP in the (0 0 0 1) plane,
even though these structures are very similar. For a given void fraction SC
offers the highest and the lowest Young's modulus depending on the direction.
For BCC at a critical void fraction a switch of the elastic behaviour is found,
as regards the direction in which the Young's modulus is maximised. For certain
crystalline void arrangements and certain directions Poisson ratios between 0
and 1 were found, including values that exceed the bounds for isotropic
materials. For subsequent investigations the full stiffness tensor for a range
of void arrangements and void fractions are provided in the supplemental
material.
