  In homogeneous and isotropic loop quantum cosmology, gravity can behave
repulsively at Planckian energy densities leading to the replacement of the big
bang singularity with a big bounce. Yet in any bouncing scenario it is
important to include non-linear effects from anisotropies which typically grow
during the collapsing phase. We investigate the dynamics of a Bianchi I
anisotropic model within the framework of loop quantum cosmology. Using
effective semi-classical equations of motion to study the dynamics, we show
that the big bounce is still predicted with only differences in detail arising
from the inclusion of anisotropies. We show that the anisotropic shear term
grows during the collapsing phase, but remains finite through the bounce.
Immediately following the bounce, the anisotropies decay and with the inclusion
of matter with equation of state $w < +1$, the universe isotropizes in the
expanding phase.
