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.
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