A guide to enriched continuum modeling: advances on wave propagation in metamaterials through the relaxed micromorphic framework

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.