New Story
Modeling Finite-Size Metamaterials with Relaxed Micromorphic Theory
by LabyrinthineMarch 23rd, 2025
Too Long; Didn't Read
This section explores relaxed micromorphic modeling for finite-size metamaterials, detailing tetragonal symmetry, elastic tensors in Voigt notation, and boundary conditions. It contrasts the classical Cauchy model with micromorphic approaches for improved metamaterial elasticity analysis.
Table of Links
1.1 A Polyethylene-based metamaterial for acoustic control
2 Relaxed micromorphic modelling of finite-size metamaterials
2.1 Tetragonal Symmetry / Shape of elastic tensors (in Voigt notation)
4 New considerations on the relaxed micromorphic parameters
4.2 Consistency of the relaxed micromorphic model with respect to a change in the unit cell’s size
4.3 Relaxed micromorphic cut-offs
6 Fitting of the relaxed micromorphic parameters with curvature (with Curl P)
6.1 Asymptotes and 6.2 Fitting
8 Summary of the obtained results
9 Conclusion and perspectives, Acknowledgements, and References
A Most general 4th order tensor belonging to the tetragonal symmetry class
B Coefficients for the dispersion curves without Curl P
C Coefficients for the dispersion curves with P
D Coefficients for the dispersion curves with P◦
2 Relaxed micromorphic modelling of finite-size metamaterials
for the classical Cauchy model, and
for the relaxed micromorphic model, where we set
The Neumann boundary condition for the classical Cauchy model are
2.1 Tetragonal Symmetry / Shape of elastic tensors (in Voigt notation)
This paper is available on arxiv under CC BY 4.0 DEED license.
[7] We write “m” for “micro” and “M” for “macro” for the corresponding elastic parameters to shorten the following expressions.
Authors:
(1) Jendrik Voss, Institute for Structural Mechanics and Dynamics, Technical University Dortmund and a Corresponding Author (jendrik.voss@tu-dortmund.de);
(2) Gianluca Rizzi, Institute for Structural Mechanics and Dynamics, Technical University Dortmund;
(3) Patrizio Neff, Chair for Nonlinear Analysis and Modeling, Faculty of Mathematics, University of Duisburg-Essen;
(4) Angela Madeo, Institute for Structural Mechanics and Dynamics, Technical University Dortmund.
L O A D I N G
. . . comments & more!
. . . comments & more!
