  A stochastic 3D microstructure model for polycrystals is introduced which
incorporates two types of twin grains, namely neighboring and inclusion twins.
They mimic the presence of crystal twins in $\gamma$-TiAl polycrystalline
microstructures as observed by 3D imaging techniques. The polycrystal grain
morphology is modeled by means of Voronoi and -- more generally -- Laguerre
tessellations. The crystallographic orientation of each grain is either sampled
uniformly on the space of orientations or chosen to be in a twinning relation
with another grain. The model is used to quantitatively study relationships
between morphology and mechanical properties of polycrystalline materials. For
this purpose, full-field Fourier-based computations are performed to
investigate the combined effect of grain morphology and twinning on the overall
elastic response. For $\gamma$-TiAl polycrystallines, the presence of twins is
associated with a softer response compared to polycrystalline aggregates
without twins. However, when comparing the influence on the elastic response, a
statistically different polycrystalline morphology has a much smaller effect
than the presence of twin grains. Notably, the bulk modulus is almost
insensitive to the grain morphology and exhibits much less sensitivity to the
presence of twins compared to the shear modulus. The numerical results are
consistent with a two-scale homogenization estimate that utilizes laminate
materials to model the interactions of twins.
