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Modeling the unusual mechanical properties of metamaterials is a challengingtopic for the mechanics community and enriched continuum theories are promisingcomputational tools for such materials. The so-called relaxed micromorphicmodel has shown many advantages in this field. In this contribution, we presentthe significant aspects related to the relaxed micromorphic model realizationwith the finite element method. The variational problem is derived anddifferent FEM-formulations for the two-dimensional case are presented. Theseare a nodal standard formulation $H^1({\cal B}) \times H^1({\cal B})$ and anodal-edge formulation $H^1({\cal B}) \times H(\operatorname{curl}, {\cal B})$,where the latter employs the N\'ed\'elec space. However, the implementation ofhigher-order N\'ed\'elec elements is not trivial and requires sometechnicalities which are demonstrated. We discuss the convergence behavior ofLagrange-type and tangential-conforming finite element discretizations.Moreover, we analyze the characteristic length effect on the differentcomponents of the model and reveal how the size-effect property is captured viathis characteristic length.

Lagrange and $H(\operatorname{curl},{\cal B})$ based Finite Element formulations for the relaxed micromorphic model