Identification of scale-independent material parameters in the relaxed\n micromorphic model through model-adapted first order homogenization

2019/08/18 by Patrizio Neff, Bernhard Eidel, Neff, Patrizio +5 · 3 citations
Engineering · #Acoustic Wave Phenomena Research #Applied Physics (physics.app-ph) #Composite Material Mechanics #FOS: Physical sciences #Railway Engineering and Dynamics

paper · pdf · doi:10.48550/arxiv.1909.13624

openalex publication_date 2019/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We rigorously determine the scale-independent short range elastic parameters\nin the relaxed micromorphic generalized continuum model for a given periodic\nmicrostructure. This is done using both classical periodic homogenization and a\nnew procedure involving the concept of apparent material stiffness of a\nunit-cell under affine Dirichlet boundary conditions and Neumann's principle on\nthe overall representation of anisotropy. We explain our idea of "maximal"\nstiffness of the unit-cell and use state of the art first order numerical\nhomogenization methods to obtain the needed parameters for a given tetragonal\nunit-cell. These results are used in the accompanying paper [16] to describe\nthe wave propagation including band-gaps in the same tetragonal metamaterial.\n

Cited by

• Static size-effects meet the dynamic scattering properties of finite-sized mechanical metamaterials: a relaxed micromorphic study with parameter identification via two-stage static-dynamic optimization
• Material data identification in generalized continua
• Breaking Scale Separation in Metamaterials' homogenization: Interface-Inertia-Enhanced Relaxed Micromorphic Model

Related

• Effective description of anisotropic wave dispersion in mechanical\n band-gap metamaterials via the relaxed micromorphic model
• Transparent anisotropy for the relaxed micromorphic model: macroscopic consistency conditions and long wave length asymptotics
• Band gaps in the relaxed linear micromorphic continuum
• Breaking Scale Separation in Metamaterials' homogenization: Interface-Inertia-Enhanced Relaxed Micromorphic Model
• On the homogenization of a new class of locally periodic microstructures in linear elasticity with residual stress