A guide to enriched continuum modeling: advances on wave propagation in metamaterials through the relaxed micromorphic framework
Abstract
This contribution provides a systematic framework for modeling the dispersive behavior of mechanical metamaterials by an enriched continua approach using the relaxed micromorphic model (RMM). We give the identification of its frequency-independent constitutive parameters from Bloch-Floquet dispersion data of the periodic metamaterial by combining analytical relations for characteristic features with a subsequent numerical optimization. Particular emphasis is placed on the underlying structure and limitations of the resulting dispersion relations, including their cut-offs, and asymptotic behavior. Finally, the transition from infinite periodic media to finite-size specimens is addressed, highlighting the role of the microscopic unit-cell cut and discussing null-Lagrangian contributions, effective interface forces, and surface Lagrangians as approaches to incorporate boundary effects.
Related
- A micromorphic constitutive framework for (non)linear softening modeling
- Discontinuous-Property Mechanical Metamaterials: A Framework for Discontinuous Lattice Dynamics
- A surrogate-assisted generative framework for on-demand inverse design of phononic metamaterials
- Quantum Thermodynamic Transformation Optics: A Unified Framework for Energy and Entropy With Application to the Casimir Force in Dissipative Metamaterials
- Data-driven material data identification in micromorphic continua
BibTeX
@misc{voss2026guide,
title = {{A guide to enriched continuum modeling: advances on wave propagation in metamaterials through the relaxed micromorphic framework}},
author = {Jendrik Voss and Svenja Hermann and Mohammad Sarhil and Patrizio Neff and Angela Madeo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39836},
eprint = {2610.39836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39836},
}
RIS
TY - UNPB
TI - A guide to enriched continuum modeling: advances on wave propagation in metamaterials through the relaxed micromorphic framework
AU - Jendrik Voss
AU - Svenja Hermann
AU - Mohammad Sarhil
AU - Patrizio Neff
AU - Angela Madeo
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39836
UR - https://arxiv.org/abs/2610.39836
AB - This contribution provides a systematic framework for modeling the dispersive behavior of mechanical metamaterials by an enriched continua approach using the relaxed micromorphic model (RMM). We give the identification of its frequency-independent constitutive parameters from Bloch-Floquet dispersion data of the periodic metamaterial by combining analytical relations for characteristic features with a subsequent numerical optimization. Particular emphasis is placed on the underlying structure and limitations of the resulting dispersion relations, including their cut-offs, and asymptotic behavior. Finally, the transition from infinite periodic media to finite-size specimens is addressed, highlighting the role of the microscopic unit-cell cut and discussing null-Lagrangian contributions, effective interface forces, and surface Lagrangians as approaches to incorporate boundary effects.
ER -