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

TL;DR

This paper presents a rigorous method to identify scale-independent elastic parameters in the relaxed micromorphic model using homogenization techniques, aiding the analysis of wave propagation in metamaterials.

Contribution

It introduces a novel procedure combining classical homogenization and apparent stiffness concepts to determine material parameters for the relaxed micromorphic model.

Findings

Successfully determines parameters for tetragonal microstructures.

Demonstrates the method's application to wave propagation analysis.

Provides a foundation for modeling band-gaps in metamaterials.

Abstract

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