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In this study, a reduced micromorphic model for multiscale materials isdeveloped. In the context of this model, multiscale materials are modeled withdeformable microstructures. The deformation energy is formed depending onmicrostrain and macroscopic strain residual fields. The constitutive equationsaccording to the reduced micromorphic model only depend on eight materialcoefficients for linear elastic materials. These material coefficients arerelated to the material micro/macro-stifnesses and the material microstructuralfeatures. The wave dispersions in multiscale materials are then derivedaccording to the reduced micromorphic model. It is revealed that this model canreflect nine dispersion curves (three acoustic modes and six optics) for atwo-scale material. To demonstrate the effectiveness of the proposed model, thewave propagation characteristics, the band structure, and the absolute bandgapfeatures of phononic materials are investigated. It is demonstrated that thereduced micromorphic model can effectively reflect the increase in the bandgapwidth with the increase in the filling factor in a composite phononic materialwith square lattices.

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