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