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Session Chair: Gerhard Starke, Universität Duisburg-Essen
Location:Auditorium Wolfsburg
Presentations
A conforming H1xHcurl finite element formulation for the relaxed micromorphic model
Mohammad Sarhil1, Lisa Scheunemann2, Patrizio Neff3, Jörg Schröder1
1Institut für Mechanik, Universität Duisburg-Essen, Germany; 2Lehrstuhl für Technische Mechanik, RPTU Kaiserslautern-Landau, Germany; 3Lehrstuhl für Nichtlineare Analysis und Modellierung, Universität Duisburg-Essen, Germany
The relaxed micromorphic model [1] is an enriched continuum that can model materials with size-effects like metamaterials. It describes the kinematics of each material point using a displacement vector and a second-order micro-distortion field and has been shown to have many advantages over other higher-order continua. It utilizes fewer material parameters due to the simplified energy compared to classical micromorphic theory. Moreover, the relaxed micromorphic model operates between two scales, i.e., linear elasticity with the micro and macro elasticity tensors. The energy functional of the relaxed micromorphic model employs the curl of the micro-distortion field, necessitating an H(Curl)-conforming finite elements.
In our presentation, we will discuss the key aspects related to the finite element formulation of the relaxed micromorphic model and compare the tangential H(Curl)-conforming formulation against the classical nodal formulation using different numerical examples [2-3].
References
[1] P. Neff, I.D. Ghiba, A. Madeo, L. Placidi and G. Rosi. A unifying perspective: the relaxed linear micromorphic continuum. Continuum Mechanics and Thermodynamics 26,639-681(2014).
[2] J. Schröder, M. Sarhil, L. Scheunemann and P. Neff. Lagrange and H(curl,B) based Finite Element formulations for the relaxed micromorphic model, Computational Mechanics 70, pages 1309–1333 (2022).
[3] M. Sarhil, L. Scheunemann, J. Schröder, P. Neff. Size-effects of metamaterial beams subjected to pure bending: on boundary conditions and parameter identification in the relaxed micromorphic model. To appear in Computational Mechanics, https://arxiv.org/abs/2210.17117 (2023).
