  In this work we present a consistent reduction of the relaxed micromorphic
model to its corresponding two-dimensional planar model, such that its capacity
to capture discontinuous dilatation fields is preserved. As a direct
consequence of our approach, new conforming finite elements for
$H^\mathrm{dev}(\mathrm{Curl},A)$ become necessary. We present two novel
$H^\mathrm{dev}(\mathrm{Curl},A)$-conforming finite element spaces, of which
one is a macro element based on Clough--Tocher splits, as well as primal and
mixed variational formulations of the planar relaxed micromorphic model.
Finally, we demonstrate the effectiveness of our approach with two numerical
examples.
