A reduced micromorphic model for multiscale materials and its applications in wave propagation

TL;DR

This paper introduces a simplified micromorphic model for multiscale materials that accurately predicts wave dispersion and bandgap features, facilitating analysis of wave propagation in complex microstructured materials.

Contribution

The study develops a reduced micromorphic model with only eight material coefficients, linking microstructure to wave behavior in multiscale materials, and demonstrates its effectiveness in phononic bandgap analysis.

Findings

The model captures nine dispersion curves in two-scale materials.

It accurately predicts bandgap width variations with filling factor.

The model efficiently reflects wave propagation characteristics in phononic materials.

Abstract

In this study, a reduced micromorphic model for multiscale materials is developed. In the context of this model, multiscale materials are modeled with deformable microstructures. The deformation energy is formed depending on microstrain and macroscopic strain residual fields. The constitutive equations according to the reduced micromorphic model only depend on eight material coefficients for linear elastic materials. These material coefficients are related to the material micro/macro-stifnesses and the material microstructural features. The wave dispersions in multiscale materials are then derived according to the reduced micromorphic model. It is revealed that this model can reflect nine dispersion curves (three acoustic modes and six optics) for a two-scale material. To demonstrate the effectiveness of the proposed model, the wave propagation characteristics, the band structure, and the absolute bandgap features of phononic materials are investigated. It is demonstrated that the reduced micromorphic model can effectively reflect the increase in the bandgap width with the increase in the filling factor in a composite phononic material with square lattices.