Novel H(symCurl)-conforming finite elements for the relaxed micromorphic sequence

divDiv sequence; H(sym Curl) finite elements; Metamaterials; Polytopal templates; Relaxed micromorphic model; Relaxed micromorphic sequence; Divdiv sequence; H(sym curl) finite element; Linear independence; Low order; Polytopal template; Computational Mechanics; Mechanics of Materials; Mechanical Engineering; Physics and Astronomy (all); Computer Science Applications

Abstract :

[en] In this work we construct novel H(symCurl)-conforming finite elements for the recently introduced relaxed micromorphic sequence, which can be considered as the completion of the divDiv-sequence with respect to the H(symCurl)-space. The elements respect H(Curl)-regularity and their lowest order versions converge optimally for [H(symCurl)∖H(Curl)]-fields. This work introduces a detailed construction, proofs of linear independence and conformity of the basis, and numerical examples. Further, we demonstrate an application to the computation of metamaterials with the relaxed micromorphic model.

Disciplines :

Mechanical engineering

Author, co-author :

SKY, Adam ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)

Neunteufel, Michael ; Institute of Analysis and Scientific Computing, Technische Universität Wien, Wien, Austria

Lewintan, Peter; Chair for Nonlinear Analysis and Modelling, Faculty of Mathematics, Universität Duisburg-Essen, Essen, Germany

ZILIAN, Andreas ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)

Neff, Patrizio; Chair for Nonlinear Analysis and Modelling, Faculty of Mathematics, Universität Duisburg-Essen, Essen, Germany

External co-authors :

yes

Language :

English

Title :

Novel H(symCurl)-conforming finite elements for the relaxed micromorphic sequence

Publication date :

2024

Journal title :

Computer Methods in Applied Mechanics and Engineering

ISSN :

0045-7825

eISSN :

1879-2138

Publisher :

Elsevier B.V.

Volume :

418

Pages :

116494

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0045782523006187?httpAccept=text/xml

Funders :

German Research Foundation
Austrian Science Fund

Funding text :

Patrizio Neff acknowledges support in the framework of the DFG-Priority Programme 2256 “Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials”, Neff 902/10-1 , Project-No. 440935806 . Michael Neunteufel acknowledges support by the Austrian Science Fund (FWF) project F65 .

Available on ORBilu :

since 20 December 2023

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