Lagrange and $H(\operatorname{curl},{\cal B})$ based Finite Element formulations for the relaxed micromorphic model
From MaRDI portal
Publication:6384506
DOI10.1007/S00466-022-02198-3arXiv2112.00382WikidataQ114229272 ScholiaQ114229272MaRDI QIDQ6384506
J. Schröder, Patrizio Neff, Lisa Scheunemann, Mohammad Sarhil
Publication date: 1 December 2021
Abstract: Modeling the unusual mechanical properties of metamaterials is a challenging topic for the mechanics community and enriched continuum theories are promising computational tools for such materials. The so-called relaxed micromorphic model has shown many advantages in this field. In this contribution, we present the significant aspects related to the relaxed micromorphic model realization with the finite element method. The variational problem is derived and different FEM-formulations for the two-dimensional case are presented. These are a nodal standard formulation and a nodal-edge formulation , where the latter employs the N'ed'elec space. However, the implementation of higher-order N'ed'elec elements is not trivial and requires some technicalities which are demonstrated. We discuss the convergence behavior of Lagrange-type and tangential-conforming finite element discretizations. Moreover, we analyze the characteristic length effect on the different components of the model and reveal how the size-effect property is captured via this characteristic length.
Could not fetch data.
This page was built for publication: Lagrange and $H(\operatorname{curl},{\cal B})$ based Finite Element formulations for the relaxed micromorphic model
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6384506)
