On the role of shear in cosmological averaging II: large voids,
  non-empty voids and a network of different voids
  We study the effect of shear on the cosmological backreaction in the context
of matching voids and walls together using the exact inhomogeneous
Lemaitre-Tolman-Bondi solution. Generalizing JCAP 1010 (2010) 021, we allow the
size of the voids to be arbitrary and the densities of the voids and walls to
vary in the range 0 < Omega_v < Omega_w < 1. We derive the exact analytic
result for the backreaction and consider its series expansion in powers of the
ratio of the void size to the horizon size, r_0/t_0. In addition, we deduce a
very simple fitting formula for the backreaction with error less than 1% for
voids up to sizes r_0 = t_0. We also construct an exact solution for a network
of voids with different sizes and densities, leading to a non-zero relative
variance of the expansion rate between the voids. While the leading order term
of the backreaction for a single void-wall pair is of order (r_0/t_0)^2, the
relative variance between the different voids in the network is found to be of
order (r_0/t_0)^4 and thus very small for voids of the observed size.
Furthermore, we show that even for very large voids, the backreaction is
suppressed by an order of magnitude relative to the estimate obtained by
treating the walls and voids as disjoint Friedmann solutions. Whether the
suppression of the backreaction due to the shear is just a consequence of the
restrictions of the used exact models, or a generic feature, has to be
addressed with more sophisticated solutions.
