  We identify effective models for thin, linearly elastic and perfectly plastic
plates exhibiting a microstructure resulting from the periodic alternation of
two elastoplastic phases. We study here both the case in which the thickness of
the plate converges to zero on a much faster scale than the periodicity
parameter and the opposite scenario in which homogenization occurs on a much
finer scale than dimension reduction. After performing a static analysis of the
problem, we show convergence of the corresponding quasistatic evolutions. The
methodology relies on two-scale convergence and periodic unfolding, combined
with suitable measure-disintegration results and evolutionary
$\Gamma$-convergence.
