  We investigate volume-element sampling strategies for the stochastic
homogenization of particle-reinforced composites and show, via computational
experiments, that an improper treatment of particles intersecting the boundary
of the computational cell may affect the accuracy of the computed effective
properties. Motivated by recent results on a superior convergence rate of the
systematic error for periodized ensembles compared to taking snapshots of
ensembles, we conduct computational experiments for microstructures with
circular, spherical and cylindrical inclusions and monitor the systematic
errors in the effective thermal conductivity for snapshots of ensembles
compared to working with microstructures sampled from periodized ensembles. We
observe that the standard deviation of the apparent properties computed on
microstructures sampled from the periodized ensembles decays at the scaling
expected from the central limit theorem. In contrast, the standard deviation
for the snapshot ensembles shows an inferior decay rate at high filler content.
The latter effect is caused by additional long-range correlations that
necessarily appear in particle-reinforced composites at high, industrially
relevant, volume fractions. Periodized ensembles, however, appear to be less
affected by these correlations. Our findings provide guidelines for working
with digital volume images of material microstructures and the design of
representative volume elements for computational homogenization.
